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

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Homework Help Overview

The discussion revolves around finding integer solutions for the equation 1007n + 1703m = 1, with a focus on the implications of the greatest common divisor (GCD) of the coefficients being 1.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express difficulty in finding integer solutions for n and m despite knowing that the GCD of 1007 and 1703 is 1, suggesting that solutions should exist. Some inquire about the relevance of external resources, such as modular multiplicative inverses, while others question how to apply this information effectively.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and expressing confusion about the application of the GCD in finding solutions. There is a request for clarification on previous attempts and the nature of the problem, indicating a collaborative effort to explore the topic further.

Contextual Notes

Participants have noted the importance of showing their attempts and identifying specific problems encountered, which may help in guiding the discussion towards productive insights.

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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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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