The diophantine equation $\left(2^{k}-1\right)\left(3^{k}-1\right)=x^{n}$ (2501.04050v1)

Abstract: In this paper, we investigate the Diophantine equation [ (2^k - 1)(3^k - 1) = x^n ] and prove that it has no solutions in positive integers $k, x, n > 2$.