Düzce Üniversitesi Matematik Bölümü Seminerleri
On The Integer Solutions of Diophantine Equation
Arzu Özkoç
Düzce University, Türkiye
Let t $\geq 2$ be an integer. In this work, we consider the integer solutions of Diophantine equation $D:x^2-(t^2-t) y^2-(4t-2)x+(4t^2-4t)y=0$ over integers and also over finite fields $Fp$ for primes $p \geq 5$. Also we will formulate the $n$−th solution $(xn,yn)$ of $D$ by means of simple continued fraction expansion. Further we derive some recurrence relations on the integer solutions of $D$.
