please explain

PROBLEM 8. Prove that a' a (mod 3) for every positive integer a PROBLEM 9. Prove that if p is a prime number greater than 3, then p- 6k+ 1, for some integer k. PROBLEM 10. Let a, b, and d be integers such that d 2 2 and a E b (mod d). Prove that ged(a, d)- gcd(b, d) PROBLEM 8. Prove that a' a (mod 3) for every positive integer a PROBLEM 9. Prove that if p is a prime number greater than 3, then p- 6k+ 1, for some integer k. PROBLEM 10. Let a, b, and d be integers such that d 2 2 and a E b (mod d). Prove that ged(a, d)- gcd(b, d)