I'm having some trouble addressing the following two questions in a text I am going through:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Cryptography / Number Theory

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