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Math Help - Prime Congruence

  1. #1
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    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"
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  2. #2
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    Quote Originally Posted by kel1487 View Post
    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).
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