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Math Help - Chinese Remainder Theorem 1

  1. #1
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    Chinese Remainder Theorem 1

    Problem:

    Solve the linear congruence 17x ≡ 3 (mod 2 * 3 * 5 * 7) by solving the system:

    a) 17x ≡ 3 (mod 2)
    b) 17x ≡ 3 (mod 3)
    c) 17x ≡ 3 (mod 5)
    d) 17x ≡ 3 (mod 7)

    I have been able to solve a), c) and d but I can't solve b. I need all solutions in order to solve the linear congruence. Can anyone help? Thank you!
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  2. #2
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    Quote Originally Posted by jmc1979 View Post
    b) 17x ≡ 3 (mod 3)
    What is the problem?
    Subtract the modulos from the right side,

    17x = 3 - 3 =0 (mod 3)
    Thus,
    17x=0(mod 3)
    Divide,
    x=0(mod 3)
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