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Math Help - Congruence

  1. #1
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    Smile Congruence

    Prove that for any integer a, a^4 ≡ 0 or 1 (mod 5)
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    Hello,
    Quote Originally Posted by terencet View Post
    Prove that for any integer a, a^4 ≡ 0 or 1 (mod 5)
    Test this out

    If a \equiv 0 (\bmod 5) then a^4 \equiv ?? (\bmod 5) ?
    If a \equiv 1 (\bmod 5) then a^4 \equiv ?? (\bmod 5) ?
    If a \equiv 2 (\bmod 5) then a^4 \equiv ?? (\bmod 5) ?
    If a \equiv 3 (\bmod 5) then a^4 \equiv ?? (\bmod 5) ?
    If a \equiv 4 (\bmod 5) then a^4 \equiv ?? (\bmod 5) ?


    Otherwise, you can use Fermat's little theorem, which says : for p prime, if a is not a multiple of p, then a^{p-1} \equiv 1 (\bmod p)
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