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2^n - 1 is divisible by p(n)

Source: 2013 Saudi Arabia IMO TST III p4

July 23, 2020

algebrapolynomialIntegerdivisible

Problem Statement

Find all polynomials

p(x)

with integer coefficients such that for each positive integer

n

, the number

2^n - 1

is divisible by

p(n)