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