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Math Help - inverse in modulo 26

  1. #1
    MHF Contributor
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    inverse in modulo 26

    Why didn't this work:

    (11,26) is 1

    11 is prime so phi of 11 is 10 but 11 to the 10 isn't congruent to 1 mod 26. It is 11 to the 12.
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  2. #2
    Junior Member
    Joined
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    Re: inverse in modulo 26

    Correct me if I'm wrong, but what you tried to do was:

    \gcd(11,26)=1,\text{ so }11^{\phi(11)}\equiv1\mod26.
    This is not correct.

    Euler's Theorem states:
    \text{ If }\gcd(a,m)=1,\text{ then }a^{\phi(m)}\equiv1\mod m.

    See?
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