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Math Help - congruence problem

  1. #1
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    congruence problem

    show that if a,b and c are integers with c>0 such that a is conguent to b (mod c), then (a,c)=(b,c)
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  2. #2
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     a \equiv b \pmod n \Rightarrow  n | (a - b)  \Rightarrow  a = b + xn where  x \in \mathbb{Z}

    so  (a,n) = (b+xn,n) = (b,n)

    The justification for the last equality is left as an exercise (it's really easy)

    Hope this helps,

    pomp.
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