How do I do this: 1) Let p be a prime number and let a ∈ Z. Prove that p∣a if and only if a≡0(mod p). 2) Use the first problem to rewrite the statement of Euclid’s Lemma (Theorem 16.6) without using ≡...

How do I do this:

1) Let p be a prime number and let a ∈ Z. Prove that p∣a if and only if a≡0(mod p).

2) Use the first problem to rewrite the statement of Euclid’s Lemma (Theorem 16.6) without using ≡ or “is congruent to.”

Euclid's Lemma Theorem 16.6: Let p ∈ N be prime and let a, b ∈ Z. If ab ≡ 0(mod p), then either a ≡ 0(mod p) or b ≡ 0(mod p).