Suppose that are two integers with gcd(m, n) = 1. Prove that there exist integers

such that

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- March 6th 2009, 08:00 AMChandru1Existence of Integers
Suppose that are two integers with gcd(m, n) = 1. Prove that there exist integers

such that - March 6th 2009, 08:34 AMOpalg
You can split this into two easier problems: find m such that , and find n such that .

- March 6th 2009, 03:07 PMChandru1Not getting
Hi--

I am not getting it. I can only think of the group Z/bZ ....(Wait) - March 7th 2009, 02:50 AMOpalg
As an illustration, here's what happens when a=5 and b=7. The equation has the solution m=6, and the equation has the solution n=4. Then the number will be congruent to 1 (mod 5) and also (mod 7), and therefore also (mod 35).

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