# Is $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ a square number for integer $x>1$

Motivated by this question.

How to prove that $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ is not a square number for integer $x>1$?

Thanks for any suggestions.

Edition by the notification of @gimusi:

The answer of this post that is mentioned by @crskhr, is provided by the dear user @Robert Z.

Thanks to all users that have been contributed in this post.

• Removed the perfect-numbers tag, as this question has got nothing to do with perfect numbers Jan 28, 2020 at 0:10