Find all integers $x$ such that $2^p + 3^p = x^2$ where $p$ an arbitrary prime number.

I think that this equation has no solution.

Thank all for help!

  • 3
    $\begingroup$ Did this question come up in something you are investigating, or is it just a random puzzle. It's very easy to make up random number theory questions like this which may turn out to be obvious or vary difficult but usually not particularly interesting. In either case you should edit the question to tell us why you think there are no solutions. $\endgroup$ – Ethan Bolker Aug 23 at 15:23

There's no solution. Consider reduction modulo 3.


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