2

Part of 2011 Canadian Students Math Olympiad

Problems(1)

Canadian Students Math Olympiad 2011 Problem 2

Source:

For a fixed positive integer

k

, prove that there exist infinitely many primes

p

such that there is an integer

w

w^2-1

is not divisible by

p

, and the order of

w

p

is the same as the order of

w

p^k

.
Author: James Rickards

quadraticsnumber theory proposednumber theory