Doubt regarding problem NMN03 of contest ISPC

I tried to solve the problem NMN03 of ISPC and on failing looked at successful submissions. I was really suprised to see them. Can anybody please tell me how to solve it and why is the ans always 0. Is there a point I am missing. link:Problem

Here is why https://math.stackexchange.com/questions/105330/equilateral-triangle-whose-vertices-are-lattice-points

The problem would have been a nightmare if the upper limit of N was declared in the order of 10^5 or 10^6. Personally, I tried the O(N^2) approach until this question struck in my mind.

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