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Math Help - university 1st yr algebra--congruence

  1. #1
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    university 1st yr algebra--congruence

    coulld anybody help me with this one? thx so much!
    or just show me the method, copying me any useful website to look it up...all sorts of help will be thanked!

    determine is the congruence has solution, if does determine the complete solution.



    thankssssss
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  2. #2
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    Congruence

    a  \equiv b (mod c)

    means that c divides a - b

    In this context, "c divides a - b" means there is an integer t so that c*t = a-b.

    In your example,

    1713x  \equiv 851 (mod 2000)

    means find x so that 2000 divides 1713x - 851.

    One such x is 227.
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  3. #3
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    Quote Originally Posted by BoboStrategy View Post
    a  \equiv b (mod c)

    means that c divides a - b

    In this context, "c divides a - b" means there is an integer t so that c*t = a-b.

    In your example,

    1713x  \equiv 851 (mod 2000)

    means find x so that 2000 divides 1713x - 851.

    One such x is 227.
    thank you very much for the "227".
    however what i am trying to dig out from this problem is how to do this kind of question in steps, but not getting the English meaning of it and figure out a number which seems meaningless to me.
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