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exists integer n such that p | n^3 - 3n + 1 where p a prime of form 9k + 1

Source: 2018 Saudi Arabia GMO TST I p2

July 31, 2020
number theorydividesdivisibleprime

Problem Statement

Let pp be a prime number of the form 9k+19k + 1. Show that there exists an integer n such that p∣n3−3n+1p | n^3 - 3n + 1.
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