Quadratic Diophantine Equation x² - (t² - t)y² - (4t - 2)x + (4t² - 4t)y = 0

Let t ≥ 2 be an integer. In this work, we consider the number of integer solutions of Diophantine equation D : x² - (t² - t)y² - (4t - 2)x + (4t² - 4t)y = 0 over Z. We also derive some recurrence relations on the integer solutions (xn; yn) of D. In the last section, we consider the same problem over nite elds Fp for primes p ≥ 5.