On the exponential Diophantine equation P^2_m+P^2_n=2^a

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This study investigates numbers that are powers of two and can be expressed as the sum of the squares of any two Pell numbers. We apply Baker’s theory of linear forms in logarithms of algebraic numbers, along with a variation of the Baker–Davenport reduction method, to solve the Diophantine equation [Formula: see text], where [Formula: see text], and [Formula: see text] are non-negative integers, as presented here. Furthermore, the maple[Formula: see text] codes used in the computations made throughout the paper are also shared.