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2025 SSMO Team Round Problems/Problem 14

Revision as of 11:32, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Find the number of ordered triples of positive integers <math>(a,b,c)</math> such that <math>a+b+c=305</math> and <math>ab+bc+ca</math> is a multiple of <math>305...")
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Problem

Find the number of ordered triples of positive integers $(a,b,c)$ such that $a+b+c=305$ and $ab+bc+ca$ is a multiple of $305$.

Solution

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