Finding the fundamental solutions of the diophantine equation ax^2+bxy+cy^2=n, where a > 0, b^2-04ac

Finding the fundamental solutions of the diophantine equation ax²+bxy+cy²=n, where a > 0, b²-4ac > 0 and is not a perfect square, n non-zero, gcd(a,b,c)=1

This program uses the bounds provided by Bengt Stolt, to find the fundamental solutions of the diophantine equation ax²+bxy+cv²=n, where n is non-zero, a > 0 and d = b² - 4ac > 0 is nonsquare. See Arkiv för Matematik, Bd. 3, Nr. 33, 381-390. It turns out that with suitable restriction on when equality occurs in the bounds, the conditions give a characterization of the fundamental solutions. This is explained in the paper On fundamental solutions of binary quadratic form equations, K.R. Matthews, J.P. Robertson and A. Srinivasan, Acta Arith. 169 (2015), 291-299.

This is a BCMath version of the BC program stolt.

Last modified 15th January 2015
Return to main page

Finding the fundamental solutions of the diophantine equation ax2+bxy+cy2=n, where a > 0, b2-4ac > 0 and is not a perfect square, n non-zero, gcd(a,b,c)=1

Finding the fundamental solutions of the diophantine equation ax²+bxy+cy²=n, where a > 0, b²-4ac > 0 and is not a perfect square, n non-zero, gcd(a,b,c)=1