If $m^x$ an integer for all naturals $m$ then $x$ and integer

Asked Jan 16 '15 at 01:07

Active Jan 16 '15 at 01:07

Viewed 55 times

I have seen this result somewhere: If $x$ is a positive real number such that $m^x$ is an integer for all natural numbers $m$, then $x$ is an integer.

It is quite interesting and I have some thoughts on it, but I have not yet solved it. By the way, is this famous?

asked Jan 16 '15 at 01:07

Prajanan Patel

1

This was asked a few weeks ago. You should be able to find it with a search. – Tim Raczkowski Jan 16 '15 at 01:10
see http://math.stackexchange.com/questions/1087841/existence-of-x-such-that-2x-a-3x-b-5x-c-for-some-integers-a-b-c/1087922#1087922 – Will Jagy Jan 16 '15 at 01:23

If $m^x$ an integer for all naturals $m$ then $x$ and integer

0 Answers0