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A Modular Arithmetic Proof Problem

  1. Sep 7, 2008 #1
    The problem statement, all variables and given/known data
    Let a, b, s, t be integers with s, t > 0. What conditions must s, t satisfy if the following statement is true:

    If a = b (mod s) and a = b (mod t), then a = b (mod st).

    The attempt at a solution
    If s | a, s | b, t | a and t | b, then st | a and st | b if and only if s, t are relatively prime. This is as far as I've gone. How should I continue?
     
  2. jcsd
  3. Sep 7, 2008 #2

    Dick

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    The statement is equivalent to s | (b-a) and t | (b-a) -> st | (b-a).
     
  4. Sep 7, 2008 #3
    Oh, that's right! I completely forgot about that. And by using what I have, I can conclude that s and t must be relatively prime.

    Thanks again.
     
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