MathDB

5

Part of 2021 Turkey MO (2nd round)

Problems(1)

Exponential function with finitely many primes

Source: Turkey National Mathematical Olympiad 2021 P5

1/6/2022
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.
number theoryprime numbers