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Part of 2017 Brazil Undergrad MO

Problems(1)

Sequence divisible by infinite primes - Brazil Undergrad MO

Source: Brazil Undergrad MO 2017 - Problem 2

11/1/2017
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.
number theoryprime numbersSequenceBrazilian Undergrad MO