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TR-MO-R1 2015 Problem 22

    x2+1≡ax(mod23)x^2 + 1 \equiv ax \pmod{23} olacak şekilde en az bir xx tam sayısının bulunmasını sağlayan kaç farklı 0≤a<230 \le a < 23 tam sayısı vardır?

    a) 5 b) 6 c) 10 d) 11 e) 12

    Official text Turkish Mathematical Olympiad, first round 2015 official paper, page 7. Quoted with source.

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