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multiples of 23 mod 2^n

Source: 2023 AIME II/15

February 16, 2023

AMCAIMEmodular arithmetic

Problem Statement

For each positive integer

n

let

a_n

be the least positive integer multiple of

23

such that

a_n\equiv1\pmod{2^n}

. Find the number of positive integers

n

less than or equal to

1000

that satisfy

a_n=a_{n+1}

.

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