(adsbygoogle = window.adsbygoogle || []).push({}); Now, I can show that if n is prime then Z/Zn is a field Let n ≥ 2 be a natural number. Show that Z/Zn is a ﬁeld if and only if n is a prime

number

a = a

b = a^{n-2}

a*b = a^{n-1}= 1 (mod n) --> Fermat's little theorem

However, I can't really seem to show that there is no multiplicative inverse for Z/Zn where n is not prime.

First question: a =/=b correct?

i know that there is the whole if gcd(a,n) = 1 then there is a multiplicative inverse, but I can't really see how to leverage this fact.

Any help would be much appreciated.

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# Mod(prime) is a field mod(non-prime) is not

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