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?
let $p$ and $q$ be relatively prime then find how many positive integers less than $pq$ exists which are relatively prime to $pq$
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elementary-number-theory
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0The answer is $(p-1)(q-1)$ if $p$ and $q$ are different prime numbers. – 2017-02-26
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2See https://en.wikipedia.org/wiki/Euler's_totient_function – 2017-02-26
1 Answers
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Hint:
By Gauß' lemmma, an integer is coprime with $pq$ if and only if it is coprime with each.