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 : x(2) - (t(2) - t)y(2) - (4t - 2)x + (4t(2) - 4t)y = 0 over Z. We also derive some recurrence relations on the integer solutions (x(n), y(n)) of D. In the last, section, we consider the same problem over finite fields F-p for primes p >= 5.