Volume 33 • Number 2 • 2010   • Quadratic Diophantine Equation x2 - ( t2 - t ) y2 - ( 4t-2 ) x + ( 4t2 - 4t ) y = 0 Arzu Özkoç and Ahmet Tekcan Abstract. 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)t + (4t2 - 4t)y = 0 over . We also derive some recurrence relations on the integer solutions (xn, yn) of D. In the last section, we consider the same problem over finite fields for primes p ≥ 5. 2000 Mathematics Subject Classification: 11D09, 11D79. Full text: PDF