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Standard sequence contains infinitely many composite integers

Source: Germany 2012 - Problem 1

December 5, 2022
number theorySequencerecursiveComposite

Problem Statement

Define a sequence (an)(a_n) by a0=−4,a1=−7a_0 =-4 , a_1 =-7 and an+2=5an+1−6ana_{n+2}= 5a_{n+1} -6a_n for n≥0.n\geq 0. Prove that there are infinitely many positive integers nn such that ana_n is composite.
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