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Recursive sequence and divisibility

Source: Prmo 2019 leg 2 P4

August 25, 2019
number theoryPRMO

Problem Statement

Let a1=24a_1=24 and form the sequence ana_n, n≥2n\geq 2 by an=100an−1+134a_n=100a_{n-1}+134. The first few terms are 24,2534,253534,25353534,…24,2534,253534,25353534,\ldots What is the least value of nn for which ana_n is divisible by 9999?
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