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Math Help - Modular Mathematics

  1. #1
    Member Maccaman's Avatar
    Joined
    Sep 2008
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    Modular Mathematics

    Hi there,
    This is an extension of a previous post and i was hoping someone could check my answer.

    I have to calculate  17^{4250} \ mod \ 190

    Here is my solution:

     \varphi (190) = 72

    Then by Euler's Theorem
     17^{72} \equiv \ 1 (mod \ 190) since gcd(17,190) = 1

    Now
    4250 = 72 * 59 + 2

    So
     17^{4250} \equiv \ (17^{72})^{59} * 17^{2} \ \equiv \ 1^{59} * 17^{2} \ \equiv \ 99 (mod \ 190)

    is that correct?

    Thanks
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by Maccaman View Post
    Hi there,
    This is an extension of a previous post and i was hoping someone could check my answer.

    I have to calculate  17^{4250} \ mod \ 190

    Here is my solution:

     \varphi (190) = 72

    Then by Euler's Theorem
     17^{72} \equiv \ 1 (mod \ 190) since gcd(17,190) = 1

    Now
    4250 = 72 * 59 + 2

    So
     17^{4250} \equiv \ (17^{72})^{59} * 17^{2} \ \equiv \ 1^{59} * 17^{2} \ \equiv \ 99 (mod \ 190)

    is that correct?

    Thanks

    I agree
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