How can the GCD of two numbers equaling 1 help find solutions for n and m?

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cloveryeah
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Homework Statement


1007n+1703m=1 when n and m are integers

Homework Equations

The Attempt at a Solution


i hv tried for so many times, but i can't find it
the GCD of 1007 and 1703 is 1, so it is possible to find n and m
 
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so that must have an ans, right?

but how to use the info given by the above link?
 
It would help a lot if you would show what you have tried and where you had problems.
 
cloveryeah said:

Homework Statement


1007n+1703m=1 when n and m are integers

Homework Equations

The Attempt at a Solution


i hv tried for so many times, but i can't find it
the GCD of 1007 and 1703 is 1, so it is possible to find n and m

HInt: when you say "the GCD of 1007 and 1703 is 1, so it is possible to find n and m", how do you know that?

Most proofs of that result that I have seen are constructive, which means that they prove the result by producing ##n## and ##m## that actually solve the problem.
 
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