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Canadian Students Math Olympiad 2011 Problem 2

Source:

July 19, 2011
quadraticsnumber theory proposednumber theory

Problem Statement

For a fixed positive integer kk, prove that there exist infinitely many primes pp such that there is an integer ww, where w2āˆ’1w^2-1 is not divisible by pp, and the order of ww in modulus pp is the same as the order of ww in modulus pkp^k.
Author: James Rickards
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