Question

Prove that if p is prime then every nonzero element has a multiplicative inverse

Answer 1

Answer:

we use , Zp is a set of positive integers.

Let m=p be prime number and x∈Zp where Zp∖{0}.

Then x is not divisible by p

⇒gcd(x,p)=1

Thus, there exists a representation a⋅x+b⋅p=1, where a,b are integers.

Well actually I can stop here because we got gcd(x,p)=1 which already shows there exists a multiplicative inverse

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