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Polynomial f in Z[x] satisfies f(p)|2^p-2

Source: 2018 RMM Shortlist N1

February 21, 2019

algebrapolynomialnumber theory

Problem Statement

Determine all polynomials

f

with integer coefficients such that

f(p)

is a divisor of

2^p-2

for every odd prime

p

.
[I]Proposed by Italy

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