Show that a positive integer n∈N is prime if and only if gcd(n,m)=1 for all $0
I know that I can write n=km+r for some k,r∈Z since n>m
and also that 1=an+bm. for some a,b∈Z
Further, I know that n>1 if I'm to show n is prime.
I'm not sure how I would go about showing this in both directions though.
Answer
Hint: If d divides n, then gcd(d,n)=d.
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