# Find a combination of n and m

1. Mar 20, 2015

### cloveryeah

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. Mar 20, 2015

### haruspex

See if http://en.m.wikipedia.org/wiki/Modular_multiplicative_inverse helps.

3. Mar 20, 2015

### cloveryeah

so that must have an ans, right?

but how to use the info given by the above link?

4. Mar 20, 2015

### HallsofIvy

Staff Emeritus
It would help a lot if you would show what you have tried and where you had problems.

5. Mar 20, 2015

### Ray Vickson

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