, Volume 23, Issue 1, pp 251-260,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 05 Nov 2009

The Diophantine equation x 2−(t 2+t)y 2−(4t+2)x+(4t 2+4t)y=0

Abstract

Let t≥1 be an integer. In this work, we consider the number of integer solutions of Diophantine equation $$x^{2}-(t^{2}+t)y^{2}-(4t+2)x+(4t^{2}+4t)y=0$$ over ℤ and also over finite fields \(\mathbb{F}_{p}\) for primes p≥5.