Question

Prove that phi (7n) = 7phi (n) iff n is multiple of 7
Please, help. I stuck at the part phi (7n) = 7 phi (n), then n is multiple of 7

Answer 1

phi (7n) = 7 phi (n), then n is multiple of 7

(proof by contradiction)

suppose \(7\nmid n\), this means \(\gcd(n,7)=1\).
since \(\phi\) is a multiplicative function, from the given equation it follows
\[\phi(7n)=7\phi(n)\\~\\\phi(7)\phi(n)=7\phi(n)\\~\\6=7\]
Contradiction, ending the proof.

Answer 2

@Loser66 do u got @ganeshie8 proof ?

Answer 3

I got him @ikram002p
@ganeshie8 thank you so much

Answer 4

=)