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

/ Authors

/ 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 $k, x, n>2$.

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

/ Authors

Bo He, Chang Liu

/ 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 $k, x, n>2$.