# let $p$ and $q$ be relatively prime then find how many positive integers less than $pq$ exists which are relatively prime to $pq$

let $p$ and $q$ be relatively prime then find how many positive integers less than $pq$ exists which are relatively prime to $pq$

I'm not good at such questions. Answer seems to be $(p-1)(q-1)$ but couldn't get why. Any help?

• The answer is $(p-1)(q-1)$ if $p$ and $q$ are different prime numbers. – ajotatxe Feb 26 '17 at 13:37
• – Crostul Feb 26 '17 at 13:37

By Gauß' lemmma, an integer is coprime with $pq$ if and only if it is coprime with each.