Track / Stage 5 / 275 of 400 #875 of 1964

12. Show that a positive integer $n$ is composite if and only if $\phi(n) \leqslant n-\sqrt{n}$.

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

I solved it I didn't Skip

Official solution

None

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.