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MathNet 2019-part-02 — 184 problems (EN–VI) Question 154

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 154

Find all positive integers $k$ such that
$$
\frac{m+n}{m^2-kmn+n^2}
$$
is not a composite number for any positive integers $m$ and $n$. (Borna Vukorepa)