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Math Help - modular arith quetion

  1. #1
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    modular arith quetion

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    .
    Last edited by yellow4321; March 6th 2008 at 05:11 AM.
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  2. #2
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    Hello, yellow4321!

    Here's a rather primitive method . . .


    Calculate: . 5^{72} \pmod{73}

    We have: . 5^9 \;=\;1,953,125 \;\equiv\;10\pmod{73}

    Then: . (5^9)^8 \;\equiv\;10^8 \pmod{73}

    . . and we find that: . 10^8 \;\equiv\;1\pmod{73}


    Therefore: . 5^{72} \;\equiv\;1\pmod{73}

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  3. #3
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    I learnt fermat's little theorem in the form a^{p-1} \equiv 1 \pmod {p} if p is prime. This applies quite easily to your problem with p = 73
    Last edited by badgerigar; January 17th 2008 at 04:34 PM. Reason: forgot math tags
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  4. #4
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    ..
    Last edited by yellow4321; March 24th 2008 at 09:36 AM.
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