TR-MO-R1 2015 Problem 18

$0 \leq n < 23^2$ koşulunu sağlayan kaç farklı $n$ tam sayısı için, $n^5 + 2n^4 + n^3 - 3n + 2$ sayısı $23^2$ ile tam bölünür?

a) 0 b) 1 c) 5 d) 23 e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2015 official paper, page 6. Quoted with source.

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