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A Modular Arithmetic Proof Problem

  • Thread starter e(ho0n3
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  • #1
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Homework Statement
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?
 

Answers and Replies

  • #2
Dick
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The statement is equivalent to s | (b-a) and t | (b-a) -> st | (b-a).
 
  • #3
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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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