Zp is a vector space iff p is prime

[CJ41]

I've got no idea how to prove it
I thought of Zp is a field iff p is prime and
Every field is a vector space over itself

 

[Steven G]

Suppose p is prime. Now try to show that Zp is a vector space (verify the definition).

Now suppose Zp is a vector space. Then show that p is prime.

Please try to do some work and post back.

 

[HallsofIvy]

A vector space over what field? It is true that Zp is a field if and only if p is prime. Are you sure that's not what you want to prove?

(Of course, any field is trivially a vector space over itself.)