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Omni-MATH / Let a₀ be a positive integer and a_(n)=5a_(n−1)+4 for all n≥1. Can a₀ be chosen so that a₅₄ is a multiple of 2013?

Problem

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problem

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?
Plain-text mathematical notation (without MathML)
Let a₀ be a positive integer and a_(n)=5a_(n−1)+4 for all n≥1. Can a₀ be chosen so that a₅₄ is a multiple of 2013?
Original LaTeX notation
Let $a_0$ be a positive integer and $a_n=5a_{n-1}+4$ for all $n\ge 1$. Can $a_0$ be chosen so that $a_{54}$ is a multiple of $2013$?

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Source and history

task_id
62489cf5-0be0-5c26-8ba0-423e5dc84aed
task_key
test--62489cf5-0be0-5c26-8ba0-423e5dc84aed
task_revision_id
1
config / split
/ test

Official source

initial import