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Find a combination of n and m

  1. Mar 20, 2015 #1
    1. The problem statement, all variables and given/known data
    1007n+1703m=1 when n and m are integers

    2. Relevant equations


    3. The attempt at a solution
    i hv tried for so many times, but i cant find it
    the GCD of 1007 and 1703 is 1, so it is possible to find n and m
     
  2. jcsd
  3. Mar 20, 2015 #2

    haruspex

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    See if http://en.m.wikipedia.org/wiki/Modular_multiplicative_inverse helps.
     
  4. Mar 20, 2015 #3
    so that must have an ans, right?

    but how to use the info given by the above link?
     
  5. Mar 20, 2015 #4

    HallsofIvy

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    It would help a lot if you would show what you have tried and where you had problems.
     
  6. Mar 20, 2015 #5

    Ray Vickson

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    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.
     
    Last edited: Mar 21, 2015
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