Key points are not available for this paper at this time.
We study the exponential Diophantine equation x²+pᵐqⁿ=2yᵖ in positive integers x, y, m, n, and odd primes p and q using primitive divisors of Lehmer sequences in combination with elementary number theory. We discuss the solvability of this equation.
Chakraborty et al. (2024) studied this question.