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In this paper, the Diophantine equation (4n) x − p y = z 2, where p is an odd prime, n ∈ Z + and x, y, z are non-negative integers, has been investigated to show that the solutions are given by (x, y, z, p) = (k, 1, 2 nk − 1, 2 nk+1 − 1) ∪ (0, 0, 0, p).
Elshahed et al. (Tue,) studied this question.
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