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Exponential function with finitely many primes

Source: Turkey National Mathematical Olympiad 2021 P5

January 6, 2022
number theoryprime numbers

Problem Statement

There are finitely many primes dividing the numbers {a⋅bn+c⋅dn:n=1,2,3,...}\{ a \cdot b^n + c\cdot d^n : n=1, 2, 3,... \} where a,b,c,da, b, c, d are positive integers. Prove that b=db=d.
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