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.

  • This is Problem 12019 in the American Math Monthly. A solution can be found in the link: AMM 12019
  • $\begingroup$ Is it possible to ask you how to search to find this pdf files? Thanks $\endgroup$ – user0410 Jul 24 '18 at 8:40
  • 1
    $\begingroup$ I was lucky to have seen this question before in AMM and was quick to show you a reference :) $\endgroup$ – crskhr Jul 24 '18 at 8:43
  • $\begingroup$ I appreciate you for addressing the link. $\endgroup$ – user0410 Jul 24 '18 at 8:48
  • 2
    $\begingroup$ By the way the solution provided is from the user @RobertZ. Many others solution a study material is available in his website, I highly suggest that as a great reference. $\endgroup$ – gimusi Jul 24 '18 at 8:53
  • $\begingroup$ @gimusi I don't see anyone by the name RobertZ in the MSE users list :( $\endgroup$ – crskhr Jul 24 '18 at 11:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.