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2025 SSMO Team Round Problems/Problem 10

Revision as of 11:32, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Anna has a three term arithmetic sequence of integers. She divides each term of her sequence by a positive integer <math>n>1</math>, and tells Bob that the three...")
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Problem

Anna has a three term arithmetic sequence of integers. She divides each term of her sequence by a positive integer $n>1$, and tells Bob that the three resulting remainders are $20$, $52$, and $R$, in some order. For how many values of $R$ is it possible for Bob to uniquely determine $n$?

Solution

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