More fun in 2015, Part 35

Find the smallest square-free positive integer \(n\) such that there exist more than 2015 Pythagorean triangles with hypotenuse \(n\). (As we all know, a Pythagorean triangle is a right triangle with positive integer sides.) As your answer, enter the largest prime factor of \(n\).

Bonus Question: How would Alexander Grothendieck have answered this question?

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