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No perfect squares in a_n=a_{n-1}^2+6a_{n-1}

Source: 2020 Caucasus Mathematical Olympiad

March 16, 2020
number theoryalgebraSequence

Problem Statement

Let ana_n be a sequence given by a1=18a_1 = 18, and an=an−12+6an−1a_n = a_{n-1}^2+6a_{n-1}, for n>1n>1. Prove that this sequence contains no perfect powers.
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