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

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The discussion centers on solving the equation 1007n + 1703m = 1 for integer values of n and m, emphasizing that the GCD of 1007 and 1703 is 1, which indicates a solution exists. Participants express frustration in finding specific integer solutions and suggest referencing modular arithmetic concepts, such as the modular multiplicative inverse. There is a call for clarification on previous attempts and the specific difficulties encountered in solving the equation. The conversation highlights the importance of constructive proofs in demonstrating the existence of solutions. Overall, the thread underscores the relationship between GCD and the solvability of linear Diophantine equations.
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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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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
See if http://en.m.wikipedia.org/wiki/Modular_multiplicative_inverse helps.
 
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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