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Primes that divide a³-3a+1

Source: Question 6 - Brazilian Mathematical Olympiad 2017

December 7, 2017
number theoryDivisibilityprimeBrazilian Math OlympiadBrazilian Math Olympiad 2017group theory

Problem Statement

6. Let aa be a positive integer and pp a prime divisor of a3−3a+1a^3-3a+1, with p≠3p \neq 3. Prove that pp is of the form 9k+19k+1 or 9k−19k-1, where kk is integer.
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