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Math Help - Congruence Problem

  1. #1
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    Congruence Problem

    Solve the congruence.

    8x ≡ 1 mod (27)

    Thanks!
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  2. #2
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    Quote Originally Posted by MathStudent1 View Post
    Solve the congruence.

    8x ≡ 1 mod (27)

    Thanks!
    gcd(8,27)=1 thus there exists a unique congruence class of solutions.

    8x = 1 = -26 mod(27)

    Thus,

    8x = -26 (mod 27)

    They share a factor of 2 which is coprime with 27, divide by it.

    4x = -13 = 14(mod 27)

    Again divide by it,

    2x = 7 (mod 27)

    Again,

    2x = - 20 (mod 27)

    x = -10 (mod 27)

    Thus,

    x = 17 (mod 27)
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  3. #3
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    Thanks TPH. I am looking through it to see if it all makes sense.
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