# Math Help - Prime Congruence

1. ## Prime Congruence

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"

2. Originally Posted by kel1487
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"
Hint: $a^2\equiv b^2 ~ (p) \implies (a-b)(a+b)\equiv 0 ~ (p)$.