TR-MO-R1 2015 Problem 27

$x^{23} - 2015^{2015}x + 23 = c$ denkleminin en az üç farklı gerçel çözümünün bulunmasını sağlayan tüm $c$ tam sayılarının aritmetik ortalaması kaçtır?

a) $-46$ b) $0$ c) $403$ d) $2015$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2015 official paper, page 8. Quoted with source.

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