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2016-2017 Fall OMO Problem 20

Source:

November 16, 2016

Problem Statement

For a positive integer

k

, define the sequence

\{a_n\}_{n\ge 0}

such that

a_0=1

and for all positive integers

n

,

a_n

is the smallest positive integer greater than

a_{n-1}

for which

a_n\equiv ka_{n-1}\pmod {2017}

. What is the number of positive integers

1\le k\le 2016

for which

a_{2016}=1+\binom{2017}{2}?

Proposed by James Lin

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