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2025 AIME I Problems/Problem 1

Revision as of 16:57, 13 February 2025 by Mathkiddus (talk | contribs) (→‎Solution 1)

Problem

Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$

Solution 1

We have, $b + 7 \mid 9b + 7$ meaning $b + 7 \mid -56$ so taking divisors of $56$ under bounds to find $b = 49, 21$ meaning our answer is $49+21=\boxed{070}.$ ~mathkiddus

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