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Sequence divisible by infinite primes - Brazil Undergrad MO

Source: Brazil Undergrad MO 2017 - Problem 2

November 1, 2017
number theoryprime numbersSequenceBrazilian Undergrad MO

Problem Statement

Let aa and bb be fixed positive integers. Show that the set of primes that divide at least one of the terms of the sequence an=a⋅2017n+b⋅2016na_n = a \cdot 2017^n + b \cdot 2016^n is infinite.
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