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BMO 2014 SL A6

Source: Balkan MO 2014 Shortlist

October 1, 2016
Sequencealgebra

Problem Statement

A6\boxed{A6}The sequence a0,a1,...a_0,a_1,... is defined by the initial conditions a0=1,a1=6a_0=1,a_1=6 and the recursion an+1=4an−an−1+2a_{n+1}=4a_n-a_{n-1}+2 for n>1.n>1.Prove that a2k−1a_{2^k-1} has at least three prime factors for every positive integer k>3.k>3.
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