Problem

Holiday Contest 2025 - Team Round - Problem 14

Let \mathcal{S} be the set of all ordered pairs (x,y) of positive integers where xy \leq 10000 satisfying

\gcd(x^3,y^3) = 11\text{ lcm}(x,y) + 3\gcd(x,y)

Compute |\mathcal{S}| (the size of \mathcal{S}).


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Problem Tags: Number theory

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