Let a,b be integers and let p be a prime number

(a) Prove that a^2 is congruent to "(b^2)mod p" implies that a is congruent to "plus or minus b mod p".

(b) Prove that a^2 is congruent to "a mod p "implies that a is congruent to "0 mod p" or a is congruent to "1 mod p"