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BALTIC-WAY 2013 Problem 19

    Let a0a_{0} be a positive integer and an=5an−1+4a_{n}=5 a_{n-1}+4, for all n≥1n \geq 1. Can a0a_{0} be chosen so that a54a_{54} is a multiple of 2013?

    Dataset text NuminaMath olympiads. Quoted with source.

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