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Math Help - Congruence

  1. #1
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    Congruence

    Dear Masters

    Can I ask why 7^879 (mod300) = 43 (mod300)?

    I thought Euler totient funcion (300) = 80 so 7^879 = 7^-1 * 7^880 .
    Then, how can I 7^-1 (mod 300)..?

    I could not get the answer

    pLeas help me out
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  2. #2
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    Re: Congruence

    Can I also ask if 49x = 3 (mod 80) is 67 (mod 80) ?
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  3. #3
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    Re: Congruence

    You can find 7^79 (mod 300) by repeated squaring - find 7^2, 7^4, 7^8, etc., then multiply the appropriate ones together.

    The answer to your second question is obvious - 49*67 = 3283 which is 3 (mod 80).

    - Hollywood
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  4. #4
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    Re: Congruence

    Hi, but the answer for 7^-1 is 43 (mod 80), and also can I ask -93 (mod 80) is 67 (mod 80)?
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