Glasnik Matematicki, Vol. 46, No.1 (2011), 1-5.

TWO EXTREME DIOPHANTINE PROBLEMS CONCERNING THE PERIMETER OF PYTHAGOREAN TRIANGLES

Allan J. MacLeod

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

Abstract.   We consider two Diophantine problems involving the perimeter of Pythagorean triangles. One has an enormous solution with the sides of the triangle > 10115, whilst the other has no solution which answers a speculation of Frenicle de Bressy.

2000 Mathematics Subject Classification.   01A45, 11-03, 11D09, 11Y50.

Key words and phrases.   Right-angled triangle, perimeter, elliptic curve.

Full text (PDF) (free access)

DOI: 10.3336/gm.46.1.01

References:

  1. L. E. Dickson, History of the theory of numbers, Vol. II. Diophantine analysis, AMS Chelsea Publishing co., New York, 1992.
    MathSciNet    

  2. T. L. Heath, Diophantus of Alexandria: A Study in the history of Greek algebra, Cambridge University Press, Cambridge, 1910.

  3. L. J. Mordell, Diophantine Equations, Academic Press, London-New York, 1969.
    MathSciNet    
Glasnik Matematicki Home Page