Literatura iz teorije brojeva

Slijedi popis literature koja se preporuča poslijediplomskim studentima, članovima Seminara za teoriju brojeva i algebru. Sve navedene knjige su dostupne i to:
(B) - središnja matematička knjižnica PMF-Matematički odjel
(N) - Nacionalna i sveučilišna knjižnica
(D) - ured A. Dujelle
(k) - netko od članova seminara ima kopiju knjige

Ako imate bilo kakvu sugestiju u svezi ovog popisa, molim da mi ju javite.

Suvoditelj seminara: Andrej Dujella



Elementarna teorija brojeva i opći udžbenici
Algebarska teorija brojeva
Analitička teorija brojeva
Algebarska geometrija
Eliptičke krivulje
Diofantske jednadžbe
Diofantske aproksimacije
Prosti brojevi, faktorizacija, primjene u kriptografiji
Neke specijalne teme
Povijest teorije brojeva, sabrana djela
Web stranice nekih kolegija iz teorije brojeva

Elementarna teorija brojeva i opći udžbenici

  1. A. Adler, J.E. Coury: The Theory of Numbers. A Text and the Source Book of Problems, Jones and Barlett Publishers, 1995. (D)

  2. G.E. Andrews: Number Theory, Dover Publications, 1994. (B,D)

  3. W.S. Anglin: The Queen of Mathematics. An Introduction to Number Theory, Kluwer Academic Publishers, 1995. (B)

  4. A. Baker: A Concise Introduction to the Theory of Numbers, Cambridge University Press, 1994. (B,D)

  5. A. Baker: A Comprehensive Course in Number Theory, Cambridge University Press, 2012. (D)

  6. A.H. Beiler: Recreations in the Theory of Numbers, Dover, 1966. (D)

  7. H. Davenport: The Higher Arithmetic, Cambridge University Press, 1999. (B)

  8. D. Duverney: Number Theory. An Elementary Introduction Through Diophantine Problems, World Scientific, 2010. (D)

  9. U. Dudley: Elementary Number Theory, Freeman, 1978. (B)

  10. H.M. Edwards: Higher Arithmetic: An Algorithmic Introduction to Number Theory, American Mathematical Society, 2008. (D)

  11. P. Erdos, J. Suranyi: Topics in the Theory of Numbers, Springer-Verlag, 2003. (B)

  12. M. Erickson, A. Vazzana: Introduction to Number Theory, Chapman & Hall/CRC, 2008. (k)

  13. G. Everest, T. Ward: An Introduction to Number Theory, Springer-Verlag, 2005. (D)

  14. E. Grosswald: Topics from the Theory of Numbers, Birkhauser, 1984. (B)

  15. F. Halter-Koch: Quadratic irrationals. An introduction to classical number theory, CRC Press, 2013.

  16. G.H. Hardy, E.M. Wright: An Introduction to the Theory of Numbers, Oxford University Press, 1980, 2008. (B,D)

  17. L.-K. Hua: Introduction to Number Theory, Springer-Verlag, 1982. (B)

  18. K. Ireland, M. Rosen: A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998. (B,D)

  19. B.W. Jones: The Theory of Numbers, Rinehart, 1957. (D)

  20. G.A. Jones, J.M. Jones: Elementary Number Theory, Springer-Verlag, 2005. (B,D)

  21. J.-M. de Koninck, A. Mercier: 1001 Problems in Classical Number Theory, American Mathematical Society, 2007. (B)

  22. E. Landau: Elementary Number Theory, Chelsea, 1966. (B)

  23. W.J. LeVeque: Elementary Theory of Numbers, Dover, 1990. (B,D)

  24. W.J. LeVeque: Fundamentals of Number Theory, Dover, 1996. (D)

  25. W.J. LeVeque: Topics in Number Theory. Volumes I and II, Dover, 2002. (D)

  26. Yu.I. Manin, A.A. Panchishkin: Introduction to Modern Number Theory, Springer-Verlag, 2005. (B)

  27. S.J. Miller, R. Takloo-Bighash: An Invitation to Modern Number Theory, Princeton University Press, 2006. (B,D)

  28. R. Mollin: Fundamental Number Theory with Applications, CRC Press, 1997. (D)

  29. T. Nagell: Introduction to Number Theory, Chelsea, 1981. (B)

  30. W. Narkiewicz: Number Theory, World Scientific, 1983. (D)

  31. I.M. Niven, H.S. Zuckerman, H.L. Montgomery: An Introduction to the Theory of Numbers, John Wiley & Sons, 1991. (B,N,D)

  32. N. Robbins: Beginning Number Theory, Wm. C. Brown Publishers, 1993. (D)

  33. H.E. Rose: A Course in Number Theory, Oxford University Press, 1995. (B,D)

  34. K.H. Rosen: Elementary Number Theory and Its Applications, Addison Wesley, 1993, 2011. (B,D)

  35. D. Shanks: Solved and Unsolved Problems in Number Theory, Chelsea, 1985. (D)

  36. J.E. Shockley: Introduction to Number Theory, Holt, Rinehart and Winston, 1967. (D)

  37. W. Sierpinski: Elementary Theory of Numbers, PNW, North Holland, 1987. (B,N)

  38. J.H. Silverman: A Friendly Introduction to Number Theory, Prentice Hall, 2001. (D)

  39. H.M. Stark: An Introduction to Number Theory, Markham, 1970. (D)

  40. W. Stein: Elementary Number Theory: Primes, Congruences, and Secrets. A Computational Approach, Springer, 2009. (D)

  41. J. Stillwell: Elements of Number Theory, Springer-Verlag, 2002. (B)

  42. I.M. Vinogradov: Elements of Number Theory, Dover, 1954. (B,D)


Algebarska teorija brojeva

  1. S. Alaca, K. S. Williams: Introductory Algebraic Number Theory, Cambridge University Press, 2004. (D)

  2. Z.I. Borevich, I.R. Shafarevich: Number Theory, Academic Press, 1986. (B)
    Zahlentheorie, Birkhauser, 1996. (B)

  3. D.A. Buell: Binary Quadratic Forms, Springer-Verlag, 1989. (D)

  4. J.W.S. Cassels: Rational Quadratic Forms, Dover, 2008. (D)

  5. H. Cohen: A Course in Computational Algebraic Number Theory, Springer-Verlag, 1993. (B,D)

  6. H. Cohen: Advanced topics in computational number theory, Springer-Verlag, 2000. (D)

  7. H. Cohn: Advanced Number Theory, Dover, 1980. (D)

  8. H. Cohn: A Classical Invitation to Algebraic Numbers and Class Fields, Springer-Verlag, 1995. (B)

  9. D.A. Cox: Primes of the Form x2 + ny2, John Wiley & Sons, 1989. (D)

  10. H.M. Edwards: Divisor Theory, Birkhäuser, 1990. (B)

  11. H.M. Edwards: Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory, Springer-Verlag, 1996. (B,D)

  12. M. Eichler: Introduction to the Theory of Algebraic Numbers and Functions, Academic Press, 1966. (B)

  13. K. Ireland, M. Rosen: A Classical Introduction to Modern Number Theory, Springer-Verlag, 1998. (B,D)

  14. G.J. Janusz: Algebraic Number Fields, American Mathematical Society, 1995. (B,D)

  15. B.W. Jones: The Arithmetic Theory of Quadratic Forms, John Wiley & Sons, 1950. (D)

  16. H. Koch: Algebraic Number Theory, Springer-Verlag, 1997. (N,D)

  17. S. Lang: Algebraic Numbers, Addison-Wesley, 1964. (B)

  18. S. Lang: Algebraic Number Theory, Springer-Verlag, 1994. (B)

  19. S. Lang: Complex Multiplication, Springer-Verlag, 1983. (B,D)

  20. D.A. Marcus: Number Fields, Springer-Verlag, 1997. (B)

  21. R.A. Mollin: Quadratics, CRC Press, 1996. (D)

  22. W. Narkiewicz: Elementary and Analytic Theory of Algebraic Numbers, Polish Scientific Publishers, 1974. (B)

  23. J. Neukirch: Algebraic Number Theory, Springer-Verlag, 1999. (B)

  24. M. Pohst, H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press, 1997. (B)

  25. H. Pollard, H.G. Diamond: The Theory of Algebraic Numbers, Dover, 1998. (D)

  26. P. Samuel: Algebraic Theory of Numbers, Dover, 2008. (D)

  27. J.-P. Serre: A Course in Arithmetic, Springer-Verlag, 1996. (B)

  28. I. Stewart, D. Tall: Algebraic Number Theory, Chapman-Hall, 1987. (B)

  29. H. Stichtenoth: Algebraic Function Fields and Codes, Springer-Verlag, 1993. (D)

  30. P. Swinnerton-Dyer: A Brief Guide to Algebraic Number Theory, Cambridge University Press, 2001. (B)

  31. L.C. Washington: Introduction to Cyclotomic Fields, Springer-Verlag, New York, 1982. (D)

  32. A. Weil: Basic Number Theory, Springer-Verlag, 1995. (B,N)

  33. S.H. Weintraub: Factorization. Unique and Otherwise, CMS, A K Peters, 2008. (D)


Analitička teorija brojeva

  1. T.M. Apostol: Introduction to Analytic Number Theory, Springer-Verlag, 1976. (B)

  2. P.T. Bateman, H.G. Diamond: Analytic Number Theory. An Introductory Course, World Scientific, 2004. (D)

  3. J.M. Borwein, P.B. Borwein: Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity, Wiley, 1987. (B)

  4. H.H. Chan: Analytic Number Theory for Undergraduates, World Scientific, 2009. (D)

  5. K. Chandrasekharan: Introduction to Analytic Number Theory, Springer-Verlag, 1969. (B,N)

  6. K. Chandrasekharan: Arithmetical Functions, Springer-Verlag, 1970. (B,D)

  7. H.M. Davenport: Multiplicative Number Theory, Springer-Verlag, 1980. (B,D)

  8. J.-M. De Koninck, F. Luca: Analytic Number Theory. Exploring the Anatomy of Integers, American Mathematical Society, 2012. (D)

  9. H. Edwards: Riemann's Zeta Function, Academic Press, 1974. (B)

  10. J. B. Friedlander, H. Iwaniec: Opera de cribo, American Mathematical Society, Providence, 2010. (B)

  11. A.O. Gelfond, Yu. V. Linnik: Elementary Methods in Analytic Number Theory, Rand McNally, 1965. (B)

  12. H. Halberstam, H.-E. Richert: Sieve Methods, Academic Press, 1974. (B)

  13. A.E. Ingham: The Distribution of Prime Numbers, Cambridge University Press, 1990. (D)

  14. A. Ivic: The Riemann Zeta-Function: The Theory of the Riemann Zeta-Function with Applications, Wiley, New York, 1985. (D)

  15. H. Iwaniec, E. Kowalski: Analytic Number Theory, American Mathematical Society, 2004. (B,D)

  16. G.J.O. Jameson: The Prime Number Theorem, Cambridge University Press, 2004. (B)

  17. E. Landau: Einfuhrung in die elementare und analytische Theorie der algebraische Zahlen und der Ideale, Chelsea, 1949. (B)

  18. H. L. Montgomery, R. C. Vaughan: Multiplicative Number Theory I. Classical Theory, Cambridge University Press, 2007. (D)

  19. D.J. Newman: Analytic Number Theory, Springer-Verlag, 1997. (B)

  20. S.J. Patterson: An Introduction to the Theory of the Riemann Zeta-Function, Cambridge University Press, 1995. (B)

  21. P. Pollack: Not Always Buried Deep, American Mathematical Society, 2009. (D)

  22. H. Rademacher: Topics in Analytic Number Theory, Springer-Verlag, 1973. (B,N)

  23. M. Ram Murty: Problems in Analytic Number Theory, Springer-Verlag, 2001. (B)

  24. J.-P. Serre: A Course in Arithmetic, Springer-Verlag, 1996. (B)

  25. I. Shparlinski: Cryptographic Applications of Analytic Number Theory, Birkhauser, 2003. (B)

  26. G. Tenenbaum: Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995. (D)

  27. G. Tenenbaum, M. Mendes France: The Prime Numbers and Their Distribution, American Mathematical Society, 2000. (D)

  28. I.M. Vinogradov: The Method of Trigonometrical Sums in the Theory of Numbers, Dover, 2004. (D)


Algebarska geometrija

  1. V. Alexeev, V.V. Nikulin: Del Pezzo and K3 Surfaces, MSJ Memoirs 15, Mathematical Society of Japan, Tokyo, 2006. (B)

  2. A. Baker, G. Wüstholz: Logarithmic Forms and Diophantine Geometry, Cambridge University Press, Cambridge, 2008. (D)

  3. W.P. Barth, K. Hulek, C.A.M. Peters, A. Van de Ven: Compact Complex Surfaces, Springer-Verlag, 2004. (B)

  4. E. Bombieri, W. Gubler: Heights in Diophantine Geometry, Cambridge University Press, 2006. (B)

  5. D. Cox, J. Little, D. O’Shea: Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer-Verlag, 2007. (B)

  6. D. Cox, J. Little, D. O’Shea: Using Algebraic Geometry, Springer-Verlag, 2005. (B)

  7. H.M. Edwards: Divisor Theory, Birkhäuser, 1990. (B)

  8. D. Eisenbud: Commutative Algebra : with a View Toward Algebraic Geometry, Springer-Verlag, 1995. (B)

  9. G. Everest, T. Ward: Heights of Polynomials and Entropy in Algebraic Dynamics, Springer-Verlag, 1999. (D)

  10. W. Fulton: Algebraic Curves. An Introduction to Algebraic Geometry, W. A. Benjamin, 1969. (D)

  11. P. Griffiths, J. Harris: Principles of Algebraic Geometry, John Wiley, 1994. (B-ruski)

  12. J. Harris: Algebraic Geometry : A First Course, Springer-Verlag, 1992. (B)

  13. R. Hartshorne: Algebraic Geometry, Springer-Verlag, 1997. (B,N)

  14. B. Hassett: Introduction to Algebraic Geometry, Cambridge University Press, 2007. (B)

  15. M. Hindry, J.H. Silverman: Diophantine Geometry. An Introduction, Springer-Verlag, 2000. (B,D)

  16. W.V.D. Hodge, D. Pedoe: Methods of Algebraic Geometry, Cambridge University Press, 1968. (B)

  17. S. Iitaka: Algebraic Geometry : An Introduction to Birational Geometry of Algebraic Varieties, Springer-Verlag, 1982. (B)

  18. E. Kunz: Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, 1985. (B)

  19. S. Lang: Introduction to Algebraic Geometry, John Wiley, 1964. (B)

  20. S. Lefschetz: Algebraic Geometry, Dover, 2005. (D)

  21. Q. Liu: Algebraic Geometry and Arithmetic Curves, Oxford University Press, 2002. (B,N)

  22. Yu.I. Manin, A.A. Panchishkin: Introduction to Modern Number Theory, Springer-Verlag, 2005. (B)

  23. D. Lorenzini: An Invitation to Arithmetic Geometry, American Mathematical Society, 1996. (B)

  24. D. Mumford: Algebraic Geometry I : Complex Projective Varieties, Springer-Verlag, 1976. (B,N)

  25. D. Mumford: The Red Book of Varieties and Schemes, Springer-Verlag, 1999. (k)

  26. M. Reid: Undergraduate Algebraic Geometry, Cambridge University Press, 1994. (N)

  27. M. Schlichenmaier: An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, Springer-Verlag, 2007. (B)

  28. I.R. Shafarevich: Basic Algebraic Geometry 1 : Varieties in Projective Space, Springer-Verlag, 1994. (B,N)

  29. I.R. Shafarevich: Basic Algebraic Geometry 2: Schemes and Complex Manifolds, Springer-Verlag, 1995. (B-ruski)

  30. J.H. Silverman: The Arithmetic of Elliptic Curves, Springer-Verlag, 1996, 2009. (B,D)

  31. K. Ueno: Algebraic Geometry 1 : from Algebraic Varieties to Schemes, American Mathematical Society, 1999. (B)

  32. U. Zannier: Some Problems of Unlikely Intersections in Arithmetic and Geometry, Princeton University Press, 2012.


Eliptičke krivulje

  1. A. Ash, R. Gross, Elliptic Tales: Curves, Counting and Number Theory, Princeton University Press, 2012. (D)

  2. A.K. Bhandari, D.D. Nagraj, R. Ramakrishnan, T.N. Venkataramana (Eds.): Elliptic Curves, Modular Forms and Cryptography, Hindustan Book Agency, 2003. (B)

  3. I. Blake, G. Seroussi, N. Smart: Elliptic Curves in Cryptography, Cambridge University Press, 1999. (D)

  4. I. Blake, G. Seroussi, N. Smart (Eds): Advances in Elliptic Curve Cryptography, Cambridge University Press, 2005. (D)

  5. J.W.S. Cassels: Lectures on Elliptic Curves, Cambridge University Press, 1995. (D)

  6. J.S. Chahal: Topics in Number Theory, Plenum Press, 1988. (D)

  7. H. Cohen, G. Frey (Eds): Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman & Hall/CRC, 2005. (D)

  8. J.B. Conrey, D.W. Farmer, F. Mezzadri, N.C. Snaith (Eds): Ranks of Elliptic Curves and Random Matrix Theory, Cambridge University Press, 2007. (D)

  9. J.E. Cremona: Algorithms for Modular Elliptic Curves, Cambridge University Press, 1997. (D)

  10. H. Darmon: Rational Points on Modular Elliptic Curves, American Mathematical Society, 2004. (B,D)

  11. F. Diamond, J. Shurman: A First Course in Modular Forms, Springer-Verlag, 2005. (B)

  12. T. Ekedahl: One Semester of Elliptic Curves, European Mathematical Society, 2006. (B)

  13. D. Hankerson, A. Menezes, S. Vanstone: Guide to Elliptic Curve Cryptography, Springer-Verlag, 2004. (D)

  14. D. Husemoller: Elliptic Curves, Springer-Verlag, 2004. (D)

  15. H. Kisilevsky, M.R. Murty (Eds.): Elliptic Curves and Related Topics, American Mathematical Society, 1994. (D)

  16. A.W. Knapp: Elliptic Curves, Princeton University Press, 1992. (B,D)

  17. N. Koblitz: Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1996. (B,D)

  18. S. Lang: Elliptic Curves: Diophantine Analysis, Springer-Verlag, 1978. (B,N)

  19. S. Ling, H. Wang, C. Xing: Algebraic Curves in Cryptography, CRC Press, 2013. (D)

  20. A. Lozano-Robledo: Elliptic Curves, Modular Forms, and Their L-functions, American Mathematical Society, 2011. (D)

  21. J. S. Milne: Elliptic Curves, BookSurge Publishers, 2006. (D)

  22. M. Rosing: Implementing Elliptic Curve Cryptography, Manning, 1999. (D)

  23. S. Schmitt, H.G. Zimmer: Elliptic Curves. A Computational Approach, de Gruyter, 2003. (D)

  24. J.-P. Serre: Lectures on the Mordell-Weil theorem, Vieweg, 1997. (B)

  25. J.H. Silverman: The Arithmetic of Elliptic Curves, Springer-Verlag, 1996, 2009. (B,D)

  26. J.H. Silverman: Advanced Topics in the Arithmetic of Elliptic Curves, Springer-Verlag, 1994. (D)

  27. J.H. Silverman, J. Tate: Rational Points on Elliptic Curves, Springer-Verlag, 1992. (B,D)

  28. L.C. Washington: Elliptic Curves: Number Theory and Cryptography, CRC Press, 2003, 2008. (B,D)


Diofantske jednadžbe

  1. T. Andreescu, D. Andrica, I. Cucurezeanu: An Introduction to Diophantine Equations. A Problem-Based Approach, Birkhäuser, 2010. (B,D)

  2. E.J. Barbeau: Pell's Equation, Springer-Verlag, 2003. (D)

  3. N.R. Bruin: Chabauty methods and covering techniques applied to generalized Fermat equations, Centrum voor Wiskunde en Informatica, 2002. (D)

  4. E.B. Burger: Exploring the Number Jungle: A Journey into Diophantine Analysis, American Mathematical Society, 2000. (D)

  5. R.D. Carmichael: The Theory of Numbers and Diophantine Analysis, Dover, 1959. (D)

  6. H. Cohen: Number Theory. Volume I: Tools and Diophantine Equations, Springer-Verlag, 2007. (D)

  7. H. Cohen: Number Theory. Volume II: Analytic and Modern Tools, Springer-Verlag, 2007. (B,D)

  8. H. Davenport: Analytic Methods for Diophantine Equations and Diophantine Inequalities, Cambridge University Press, 2005. (D)

  9. J.H. Evertse: Upper Bound for the Numbers of Solutions of Diophantine Equations, Centrum voor Wiskunde en Informatica, 1983. (k)

  10. I. Gaal: Diophantine Equations and Power Integral Bases, Birkhauser, 2002. (B)

  11. A.O. Gelfond: The Solution of Equations in Integers, P. Noordhoff, 1960. (B)

  12. M.J. Jacobson, H.C. Williams: Solving the Pell Equation, Springer, 2009. (D)

  13. W.J. LeVeque: Studies in Number Theory, Mathematical Association of America, 1969.(B)

  14. R.C. Mason: Diophantine Equations over Function Fields, Cambridge University Press, 1984. (B,N)

  15. L.J. Mordell: Diophantine Equations, Academic Press, 1969. (k)

  16. A.J. van der Poorten, J.H. Loxton (Eds.): Diophantine Analysis, Cambridge University Press, 1986. (D)

  17. J.L. Ramirez Alfonsin: The Diophantine Frobenius Problem, Oxford University Press, 2005. (B)

  18. N. Saradha (Ed.): Diophantine Equations, 2005 Mumbai conference in honour of T.N. Shorey, Tata Institute of Fundamental Research, 2007. (D)

  19. W.M. Schmidt: Equations over Finite Fields: An Elementary Approach, Springer-Verlag, 1976. (B)

  20. W.M. Schmidt: Diophantine Approximations and Diophantine Equations, Springer-Verlag, 1996. (D)

  21. R. Schoof: Catalan's Conjecture, Springer, 2008. (D)

  22. T.H. Shorey, R. Tijdeman: Exponential Diophantine Equations, Cambridge University Press, 1986. (D)

  23. W. Sierpinski: Pythagorean Triangles, Yeshiva University, 1962. (B)

  24. T. Skolem: Diophantische Gleichungen, Chelsea, 1950. (B)

  25. N.P. Smart: The Algorithmic Resolution of Diophantine Equations, Cambridge University Press, 1998. (B,D)

  26. V.G. Sprindzuk: Classical Diophantine Equations, Springer-Verlag, 1993. (k)

  27. J. Steuding: Diophantine Analysis, Chapman & Hall/CRC, 2005. (D)

  28. B.M.M. de Weger: Algorithms for Diophantine Equations, Centrum voor Wiskunde en Informatica, 1989. (k)

  29. U. Zannier: Some applications of Diophantine Approximation to Diophantine Equations, Forum Editrice, Udine, 2003. (D)

  30. U. Zannier: Lecture Notes on Diophantine Analysis, Edizioni della Normale, 2009. (D)


Diofantske aproksimacije

  1. A. Baker: Transcendental Number Theory, Cambridge University Press, 1990. (B,N)

  2. A. Baker, G. Wüstholz: Logarithmic Forms and Diophantine Geometry, Cambridge University Press, Cambridge, 2008. (D)

  3. J. Borwein, A. van der Poorten, J. Shallit, W. Zulidin: Neverending Fractions. An Introduction to Continued Fractions, Cambridge University Press, Cambridge, 2014. (D)

  4. Y. Bugeaud: Approximation by Algebraic Numbers, Cambridge University Press, 2004. (B)

  5. Y. Bugeaud: Distribution modulo one and Diophantine approximation, Cambridge University Press, 2012. (D)

  6. E.B. Burger, R. Tubbs: Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory, Springer-Verlag, 2004. (D)

  7. J.W.S. Cassels: An Introduction to Diophantine Approximation, Cambridge University Press, 1965. (k)

  8. D. Hensley: Continued Fractions, World Scientific, 2006. (D)

  9. A.Ya. Khinchin: Continued Fractions, Dover, 1997. (D)

  10. J. F. Koksma: Diophantische Approximationen, Springer, 1936. (D)

  11. S. Lang: Introduction to Diophantine Approximations, Addison-Wesley, 1966. (B)

  12. L. Lovasz: An Algorithmic Theory of Numbers, Graphs and Convexity, SIAM, 1986. (D)

  13. I. Niven: Diophantine Approximations, John Wiley & Sons, 1963. (B,D)

  14. C.D. Olds: Continued Fractions, Random House, 1963. (B,D)

  15. O. Perron: Die Lehre von den Kettenbruchen, Teubner, 1954. (B)

  16. A. M. Rockett, P. Szusz: Continued Fractions, World Scientific, 1992. (D)

  17. W.M. Schmidt: Diophantine Approximation, Springer-Verlag, 1996. (B,D)

  18. W.M. Schmidt: Diophantine Approximations and Diophantine Equations, Springer-Verlag, 1996. (D)

  19. Th. Schneider: Einfuhrung in die transzendenten Zahlen, Springer-Verlag, 1957. (B)

  20. M. Waldschmidt: Diophantine Approximation on Linear Algebraic Groups, Springer-Verlag, 2000. (B)

  21. U. Zannier: Some applications of Diophantine Approximation to Diophantine Equations, Forum Editrice, 2003. (D)

  22. U. Zannier: Lecture Notes on Diophantine Analysis, Edizioni della Normale, 2009. (D)


Prosti brojevi, faktorizacija, primjene u kriptografiji

  1. E. Bach, J. Shallit: Algorithmic Number Theory, Volume I: Efficient Algorithms, MIT Press, 1996. (D)

  2. M.W. Baldoni, C. Ciliberto, G.M. Piacentini Cattaneo: Elementary Number Theory, Cryptography and Codes, Springer, 2009. (B)

  3. D.M. Bressoud: Factorization and Primality Testing, Springer-Verlag, 1989. (D)

  4. J.P. Buhler, P. Stevenhagen (Eds.): Algorithmic Number Theory. Lattices, Number Fields, Curves and Cryptography, Cambridge University Press, 2008.

  5. H. Cohen: A Course in Computational Algebraic Number Theory, Springer-Verlag, 1993. (B,D)

  6. R. Crandall, C. Pomerance: Prime Numbers: A Computational Perspective, Springer-Verlag, 2001. (B,D)

  7. A. Das: Computational Number Theory, CRC Press, 2013. (D)

  8. P. Garrett, D. Lieman (Eds.): Public-Key Cryptography, American Mathematical Society, Providence, 2005. (B)

  9. P.J. Giblin, Primes and Programming, an Introduction to Number Theory with Computing, Cambridge University Press, 1993. (k)

  10. J. Hoffstein, J. Pipher, J. H. Silverman: An Introduction to Mathematical Cryptography, Springer, 2008. (D)

  11. M. Kac: Statistical Independence in Probability, Analysis and Number Theory, Mathematical Association of America, 1959. (B)

  12. N. Koblitz: A Course in Number Theory and Cryptography, Springer-Verlag, 1994. (B)

  13. N. Koblitz: Algebraic Aspects of Cryptography, Springer-Verlag, Berlin, 1999. (D)

  14. E. Kranakis: Primality and Cryptography, Teubner, John Wiley, 1987. (B)

  15. A.K. Lenstra, H.W. Lenstra, Jr. (Eds.): The Development of the Number Field Sieve, Springer-Verlag, 1993. (B)

  16. A. Pethö: Algebraische Algorithmen, Vieweg, 1999. (B,D)

  17. C. Pomerance (Ed.): Cryptology and Computational Number Theory, Proceedings of Symposia in Applied Mathematics, Vol. 42, American Mathematical Society, Providence, 1990. (D)

  18. P. Ribenboim: The Book of Prime Number Records, Springer-Verlag, 1989. (D)

  19. H. Riesel: Prime Numbers and Computer Methods for Factorization, Birkhauser, 1994. (B)

  20. M.R. Schroeder: Number Theory in Science and Communication, Springer-Verlag, 1991. (B,N)

  21. V. Shoup: A Computational Introduction to Number Theory and Algebra, Cambridge University Press, 2005. (D)

  22. N. Smart: Cryptography. An Introduction, McGraw-Hill, 2002. (D)

  23. D. R. Stinson: Cryptography. Theory and Practice, CRC Press, 1996, 2002, 2005. (B,D)

  24. G. Tenenbaum, M. Mendes France: The Prime Numbers and Their Distribution, American Mathematical Society, 2000. (D)

  25. S. S. Wagstaff, Jr.: Cryptanalysis of Number Theoretic Ciphers, Chapman and Hall/CRC Press, 2002. (B)

  26. S.Y. Yan: Number Theory for Computing, Springer-Verlag, 2002. (B,D)

  27. S.Y. Yan: Computational Number Theory and Modern Cryptography, Wiley, 2013. (D)


Neke specijalne teme

  1. M. Aigner: Markov's Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings, Springer, 2013. (D)

  2. J.-P. Allouche, J. Shallit: Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, 2003. (B)

  3. G.E. Andrews, B.C. Berndt: Ramanujan's Lost Notebook, Springer-Verlag, 2005. (B)

  4. V. Berthe, M. Rigo: Combinatorics, Automata and Number Theory, Cambridge University Press, 2010. (B)

  5. P. Borwein: Computational Excursions in Analysis and Number Theory, Springer-Verlag, 2002. (B)

  6. W. Bosma, J. Cannon (Eds.): Discovering Mathematics with Magma. Reducing the Abstract to the Concrete, Springer-Verlag, 2006. (D)

  7. J.W. Cassels: An Introduction to the Geometry of Numbers, Springer-Verlag, 1997. (B,N,D)

  8. J.W.S. Cassels, E.V. Flynn: Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, Cambridge University Press, 1996. (D)

  9. K. Dajani, C. Kraaikamp: Ergodic Theory of Numbers, Cambridge University Press, 2002. (B)

  10. G. Everest, A. van der Poorten, I. Shparlinski, T. Ward: Recurrence sequences, AMS Surveys and Monographs, Vol. 104, 2003. (B)

  11. S. Finch: Mathematical Constants, Cambridge University Press, 2003. (D)

  12. F.Q. Gouvea, p-adic Numbers: An Introduction, Springer-Verlag, 2003. (B)

  13. E. Grosswald: Representations of Integers as Sums of Squares, Springer-Verlag, 1985. (B)

  14. R.K. Guy: Unsolved Problems in Number Theory, Springer-Verlag, 2004. (B,D)

  15. H. Halberstam, K.F. Roth: Sequences, Springer-Verlag, 1983. (B)

  16. Y. Hellegouarch: Invitation to the Mathematics of Fermat-Wiles, Academic Press, 2002. (D)

  17. P.-C. Hu, C.-C. Yang, Value Distribution Theory Related to Number Theory, Birkhäuser, 2006. (B)

  18. L.-K. Hua and W. Yuan: Applications of Number Theory to Numerical Analysis, Springer-Verlag, 1981. (B)

  19. N. Koblitz: p-adic Numbers, p-adic Analysis, and Zeta Functions, Springer-Verlag, 1996. (B)

  20. T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, 2001. (D)

  21. E. Kratzel: Lattice Points, VEB Deutscher Verlag der Wissenschaften, 1988. (D)

  22. M. Krizek, F. Luca and L. Somer: 17 Lectures on Fermat Numbers, Springer-Verlag, 2001. (D)

  23. R. Lidl, G.K. Mullen, G. Turnwald: Dickson polynomials, Longman, 1993. (k)

  24. Yu.V. Matiyasevich: Hilbert's Tenth Problem, MIT Press, 1993. (D)

  25. K. Ono: The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series, CBMS Monograph 102, AMS, 2004. (B)

  26. W. Narkiewicz: Classical Problems in Number Theory, PWN, 1986. (B)

  27. M.B. Nathanson: Additive Number Theory, Springer-Verlag, 1996. (D)

  28. P. Q. Nguyen, B. Vallee (Eds.): The LLL algorithm. Survey and Applications, Springer, 2010. (D)

  29. A.J. van der Poorten: Notes on Fermat's Last Theorem, Wiley, 1996. (D)

  30. P. Ribenboim: 13 Lectures on Fermat's Last Theorem, Springer-Verlag, 1979. (D)

  31. F. Rodriguez Villegas: Experimental Number Theory, Oxford University Press, 2007. (D)

  32. M. Rosen: Number Theory in Function Fields, Springer-Verlag, 2002. (D)

  33. A. Schinzel: Selected Topics on Polynomials, University of Michigan Press, 1982. (D)

  34. A. Schinzel: Polynomials with Special Regard to Reducibility, Cambridge University Press, 2000. (B)

  35. I.E. Shparlinski: Finite Fields: Theory and Computation. The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography, Kluwer, 1999. (B)

  36. J.H. Silverman: The Arithmetic of Dynamical Systems, Springer-Verlag, 2007. (D)

  37. W.A. Stein: Modular Forms: A Computational Approach, American Mathematical Society, Providence, 2007. (D)

  38. S. Vajda: Fibonacci & Lucas Numbers, and the Golden Section, theory and applications, Ellis Horwood, 1989. (D)

  39. N.V. Vorobiev: Fibonacci Numbers, Birkhauser, 2002. (B)

  40. G. Wüstholz (Ed.): A Panorama of Number Theory or The View from Baker's Garden, Cambridge University Press, 2002. (B)


Povijest teorije brojeva, sabrana djela

  1. I.G. Bashmakova: Diophantus and Diophantine Equations, Mathematical Association of America, 1998. (D)

  2. L.E. Dickson: History of the Theory of Numbers, Volume 1: Divisibility and Primality, Chelsea, 1966. (D)

  3. L.E. Dickson: History of the Theory of Numbers, Volume 2: Diophantine analysis, Chelsea, 1966. (D)

  4. L.E. Dickson: History of the Theory of Numbers, Volume 3: Quadratic and Higher Forms, Chelsea, 1966. (B,D)

  5. C.F. Gauss: Disquisitiones Arithmeticae, Yale University Press, 1965. (D)

  6. T.L. Heath: Diophantus of Alexandria: A study in the history of Greek Algebra. With a supplement containing an account of Fermat's theorems and problems connected with Diophantine analysis and some solutions of Diophantine problems by Euler, Powell's Bookstore; Martino Publishing, 2003. (D)

  7. Collected papers of Wilhelm Ljunggren, Volumes 1,2, (P. Ribenboim, Ed.), Queen's University, 2003. (B)

  8. Collected Papers of Trygve Nagell, Volumes 1,2,3,4, (P. Ribenboim, Ed.), Queen's University, 2002. (B)

  9. W. Narkiewicz, Rational Number Theory in the 20th Century. From PNT to FLT, Springer, 2012.

  10. O. Ore: Number Theory and Its History, Dover, 1988. (D)

  11. Andrzej Schinzel, Selecta, Volume I: Diophantine Problems and Polynomials, (H. Iwaniec, W. Narkiewicz and J. Urbanowicz, Eds.), European Mathematical Society, 2007. (B)

  12. Andrzej Schinzel, Selecta, Volume II: Elementary, Analytic and Geometric Number Theory, (H. Iwaniec, W. Narkiewicz and J. Urbanowicz, Eds.), European Mathematical Society, 2007. (B)

  13. A. Weil: Number Theory: An Approach through History from Hammurapi to Legendre, Birkhäuser, 1987. (D)


Web stranice nekih kolegija iz teorije brojeva

  1. W. Chen: Elementary Number Theory, Imperial College, University of London

  2. M. Filaseta: Elementary Number Theory, University of South Carolina

  3. W. Stein: Elementary Number Theory, Harvard University

  4. Pete L. Clark: Number Theory, University of Georgia

  5. F. Lemmermeyer: Algebraic Number Theory, Bilkent University

  6. J. Milne: Algebraic Number Theory, University of Michigan

  7. W. Stein: Introduction to Algebraic Number Theory, Harvard University

  8. W. Chen: Distribution of Prime Numbers, Imperial College, University of London

  9. N. Elkies: Introduction to Analytic Number Theory, Harvard University

  10. K. Kedlaya: Analytic Number Theory, MIT

  11. J. Milne: Algebraic Geometry, University of Michigan

  12. E. Goins: Elliptic Curves, Purdue University

  13. I. Kiming: Introduction to Elliptic Curves, University of Copenhagen


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