2004 OIM Problems/Problem 3

Problem

Let $n$ and $k$ be positive integers such that either $n$ is odd or $n$ and $k$ are even. Prove that there are integers $a$ and $b$ such that

\[gcd(a, n) = gcd(b, n) = 1, k = a + b\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions