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Proofs and numbers

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Use Fermat's Little Theorem to find the remainder on division 5^120 by 19.

  • Proofs and numbers -

    According to Fermat's Little Theorem:

    5^18 = 1 Mod 19

    This means that in the exponent you can reduce Mod 18.

    120 Mod 18 = 20*6 Mod 18 = 2*6 Mod 18 = 12 Mod 18

    5^3 Mod 19 = 125 Mod 19 =

    (20*6+5) Mod 19 = 6+5 = 11

    5^6 Mod 19 = 11^2 = (6*20+1) Mod 19 = 7

    5^12 Mod 19 = 7^2 Mod 19 = 49 Mod 19 = 11

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