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Math Help - systems of congruences

  1. #1
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    systems of congruences

    Hello. I am completely stumped by this problem:

    x = a1 (mod m1)
    x = a2 (mod m2)
    ...
    x = an (mod mn)

    Let mj be arbitrary positive integers. Show that there is a simultaneous solution of this system if and only if ai= aj (mod(mi, mj)) for all pairs of the indices i,j for which 1 <= i < j <= r

    Thanks for the help.
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  2. #2
    MHF Contributor

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    What do you mean by "mod(mi,mj)"?
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  3. #3
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    I mean the greatest common divisor of mi and mj as the modulo. mi is m_{i} and mj is m_{j}
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  4. #4
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    This in the commonly known Chinese Remainder Theorem.
    Use Google to get some explanations.
    There are proofs available on the internet.
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