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On the Diophantine equation x<sup>2</sup>+ 2<sup>α</sup>13<sup>β</sup>= y<sup>n</sup>
We find all the solutions of the Diophantine equation $$x^2 + 2^{\alpha} 13^{\beta}= y^n$$ in positive integers $x,y,\alpha,\beta,n\ge 3$ with $x$ and $y$ coprime.