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2004 OIM Problems/Problem 3

Revision as of 17:27, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>n</math> and <math>k</math> be positive integers such that either <math>n</math> is odd or <math>n</math> and <math>k</math> are even. Prove that there...")
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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

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