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Recursion

Source: 2013 Baltic Way, Problem 19

December 31, 2013
algebrapolynomialmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

Let a0a_0 be a positive integer and an=5an−1+4a_n=5a_{n-1}+4 for all n≥1n\ge 1. Can a0a_0 be chosen so that a54a_{54} is a multiple of 20132013?
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