N1

Part of 2018 Romanian Master of Mathematics Shortlist

Problems(1)

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

Source: 2018 RMM Shortlist N1

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

algebrapolynomialnumber theory