I JUST NEED 3) AND 4) DONE, DO NOT LEAVE 3) AND 4) OUT OF YOUR WORK

On the possibility of division in Zp, the quotient set of integers modulo p)

1) Letting p N and that p greater/= to 2, prove that if p is not prime then there exists [a], [b] Zp such that [a] is not equal to [0], [b] is not equal to [0] and finally [a] [b] = [0].

[We must now display that if p IS prime, then this statement can not happen, and every nonzero element has some multiplicative inverse.]

2)Letting p N be a prime number, and letting a {1,...,p 1}. We must now show that there exists k, l N with k > l such that a_k and a_l are congruent modulo p.

3) With k, l from #2), show that p | (a^k-l 1) and as a result, [a]_k-l = [1], where we have stated that

[a]_k-l =[a][a][a] (where the amount of [a]'s is (k-l) times)

Then fourth, 4) Deduce that when p N is prime, if [a], [b] Zp and [a] is not equal to [0] and [b] is not equal to [0], then [a][b] is NOT equal to [0].

I REALLY need 2-4 the most! Please do this