Thread: Question involving congruences and gcd's

Let a, x, n, y in Z, n>1. Prove that if ax is congruent to ay(mod n), then x is congruent to y (mod n/d), where d = (a,n).

Question: How do I do the congruence equal sign thing, and other stuff like that. Also, a, x, n, y in Z. How do I do the symbol to show they are in the set Z? Thanks.

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To produce these math symbols, take a look at this tutorial: LaTex Tutorial

Basically, wrapping coding around [tex][/tex] will produce these images. For example, is produced by [tex]x^{2} \equiv 2 \; (\text{mod } 4)[/tex]. If you want to see the coding behind an image, just click on it!

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As for your question: for some

Since , we can divide both sides by :

Now use the fact that if and , then .

Can you finish?