Problem #WSP-5316

Problem

Let $ϕ (n)$ be Euler’s function. Namely $ϕ (n)$ counts how many integers from $1$ to $n$ inclusive are coprime with $n$ . For two natural numbers $m$ , $n$ such that $gcd (m, n) = 1$ , prove that $ϕ (m n) = ϕ (m) ϕ (n)$ .

To see the solution register and get verified.