(untitled) (European Journal of Pure and Applied Mathematics, 2023)
Let P(t)_i^±=t^2k ± i t^m be a non square polynomial and Q(t)_i^±=4k^2t^4k-2+i^2m^2t^2m-2 ± 4imkt^2k+m-2 -4t^2k 4it^m -1 be a polynomial, such that k ≥ 2m and i 1,2 brace . In this paper, we consider the number of integer solutions of Diophantine equation E : x^2-P(t)_i^±y^2-2P’(t)_i^±x+4 P(t)_i^± y +Q(t)_i^±=0. We extend a previous results given by A. Tekcan and A. Chandoul et al. . We also derive some recurrence relations on the integer solutions of a Pell equation.