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(a^n + b^n + 1) is divisible by d for all positive integers n

Source: Dutch IMO TST 2016 p2

August 30, 2019

number theorydivisibledivisorexponential

Problem Statement

Determine all pairs

(a, b)

of integers having the following property: there is an integer

d \ge 2

such that

a^n + b^n + 1

is divisible by

d

for all positive integers

n