Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 1-7.

SQUARE EULERIAN QUADRUPLES

Allan J. MacLeod

Mathematics and Statistics Group, University of the West of Scotland, High St., Paisley, Scotland, PA1 2BE, UK
e-mail: allan.macleod@uws.ac.uk


Abstract.   We consider the problem of finding four different rational squares, such that the product of any two plus the sum of the same two always gives a square. We give some historical background to this problem and exhibit the small number of solutions found so far.

2010 Mathematics Subject Classification.   11A99, 11D09, 11G05, 11Y50.

Key words and phrases.   Squares, Eulerian quadruples, elliptic curves.


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References:

  1. L. E. Dickson, History of the Theory of Numbers, Vol. 2 Diophantine Analysis, AMS, Chelsea, New York, 1992.
    MathSciNet

  2. A. Dujella, An extension of an old problem of Diophantus and Euler, Fibonacci Quarterly 37 (1999), 312-314.
    MathSciNet

  3. A. Dujella, An extension of an old problem of Diophantus and Euler. II, Fibonacci Quarterly 40 (2002), 118-123.
    MathSciNet

  4. L. J. Mordell, Diophantine Equations, Academic Press, New York, 1968.
    MathSciNet


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