KöMaL problem A, 2026

Number theory Difficulty 6.0 National Olympiad Prove it Hungary

Prove that for any integers $k>10$ and $n>k^4$ , among the integers $({n+1^2})$ , $({n+2^2})$ , $({n+3^2})$ , $\ldots$ , $({n+k^2})$ , there is at least one that has a prime divisor greater than $k$ .

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