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Source: 2018 AIME I #2

March 7, 2018

AMCAIMEAIME I2018 AIME I

Problem Statement

The number

n

can be written in base

14

as

\underline{a}

\underline{b}

\underline{c}

, can be written in base

15

as

\underline{a}

\underline{c}

\underline{b}

, and can be written in base

6

as

\underline{a}

\underline{c}

\underline{a}

\underline{c}

, where

a > 0

. Find the base-

10

representation of

n

.

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