2004 OIM Problems/Problem 3
Problem
Let 
and 
be positive integers such that either is odd or and are even. Prove that there are integers 
and 
such that
![\[gcd(a, n) = gcd(b, n) = 1, k = a + b\]](http://latex.artofproblemsolving.com/f/d/a/fda3ecd7a0be9986a0ebb42844719b6ab4d3c265.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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