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Math Help - Fermatís Theorem

  1. #1
    Junior Member
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    Fermatís Theorem

    Hi Guys,

    In my information security class, been receiving a couple of these questions, i am able to do it by breaking them down and calculating them.

    However my teacher told me NOT to calculate them and i can answer it just by looking at the questions.

    If you guys can break any of these down with as much information as you can that would be really great.

    Use Fermatís Theorem compute:

     2^6\ mod  \7

    97^{130} \mod \131

    51^{22} \mod \23
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: Fermatís Theorem

    Quote Originally Posted by extatic View Post
    Hi Guys,

    In my information security class, been receiving a couple of these questions, i am able to do it by breaking them down and calculating them.

    However my teacher told me NOT to calculate them and i can answer it just by looking at the questions.

    If you guys can break any of these down with as much information as you can that would be really great.

    Use Fermatís Theorem compute:

     2^6\ mod  \7

    97^{130} \mod \131

    51^{22} \mod \23
    Fermat's [little] theorem: if p is prime and p doesn't devide a then a^{p-1}\equiv\ 1\ \text{mod}\ p...

    Your cases...

    a) 7 is prime and 7 doesn't devide 2 \implies 2^{6} \equiv\ 1\ \text{mod}\ 7

    b) 131 is prime and 131 doesn't devide 97 \implies 97^{130} \equiv\ 1\ \text{mod}\ 131

    a) 23 is prime and 23 doesn't devide 51 \implies 51^{22} \equiv\ 1\ \text{mod}\ 23

    Kind regards

    \chi \sigma
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  3. #3
    Junior Member
    Joined
    May 2010
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    Re: Fermatís Theorem

    thank you soo much, awesome help.
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