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2025 SSMO Relay Round 5 Problems/Problem 3

Revision as of 11:44, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR.</math> How many positive integers <math>n</math> satisfy <cmath>\operatorname{lcm}(\operatorname{gcd}(n, n^2 + T^2), \operatorname{gcd}(T, n^...")
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Problem

Let $T = TNYWR.$ How many positive integers $n$ satisfy \[\operatorname{lcm}(\operatorname{gcd}(n, n^2 + T^2), \operatorname{gcd}(T, n^2 + T^2)) = \operatorname{lcm}(n, T)?\]

Solution

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