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Math Help - Units and Systems of Congruences

  1. #1
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    Units and Systems of Congruences

    1) Make a list of the units in Z16, and with each unit give its multiplicative inverse.

    2) Solve the following system of congruences
    X=2 (mod 3)
    X=3 (mod 5)
    X=6 (mod 7)
    3) Solve the following system of congruences
    X=2 (mod 3)
    X=3 (mod 5)
    X=4 (mod 7)
    X=5 (mod 11)
    Any help would be great.
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  2. #2
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    Use Chinese Remainder Theorem for (2),(3).
    For (2), your a_1, a_2, a_3 in the above link are 2,3,6, respectively.
    Your m_1, m_2, m_3 are 3,5,7 (relative primes).
    Your M would be 3*5*7 = 105.

    You need to calculate each b's value in the above link and calculate x (Verify your answer is correct).
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