if , then has a unique sol.

By Bezout, there exist such that

Now, we can write that as:

Correct?

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- Jun 22nd 2011, 08:47 PMdwsmithif (a,m)=1, then ax\equiv 1 (mod m) has a unique sol.
if , then has a unique sol.

By Bezout, there exist such that

Now, we can write that as:

Correct? - Jun 22nd 2011, 09:05 PMtopspin1617Re: if (a,m)=1, then ax\equiv 1 (mod m) has a unique sol.
Hmm...

I don't know about that. What we are trying to prove is that there is a unique value for (up to congruence modulo ) satisfying (where are fixed). I don't think that what you have done gives us the uniqueness.

Try this: suppose there exist such that . We try to prove that .

It's fairly simple: what happens if you multiply the congruence by ?