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**1.**Show that n is a prime number iff whenever a,b ∈ Zn with ab=0, we must have that a=0 or b=0.

**2.**Show that n is a prime number iff for every a,b,c ∈ Zn satisfying a not =0, and ab=ac, we have that b=c.

There were some other similar questions that addressed showing two numbers are relatively prime by showing that gcd(a,n)=1, which was a little difficult to start, but I think I managed to get through them. However, I am stuck with these. Not sure how to begin to prove.

Any help is appreciated.