grandes-ecoles 2016 QIV.B.2

grandes-ecoles · France · centrale-maths2__pc Proof Direct Proof of an Inequality
We consider throughout the rest of this part a real $\alpha$. We assume that for every prime number $p$, $p^\alpha$ is a natural number. We propose to show that $\alpha$ is then a natural number.
Show that $\alpha$ is positive or zero.
We consider throughout the rest of this part a real $\alpha$. We assume that for every prime number $p$, $p^\alpha$ is a natural number. We propose to show that $\alpha$ is then a natural number.

Show that $\alpha$ is positive or zero.