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while trying to answer a home work question I came up with an unrelated equation, although it is very trivial it seemed interesting to me:

If n is an integer not divisible by 3 and not equal to 0, then [(2*(n^2)+1] MUST be divisible by 3.

I tried to proof it using the fact that

(n^3)/3 + (n^2)/2 + n/6 is always an integer. It seemed good but I stopped in the second page!

So my question is there a nicer shorter way to proof it?

Thanks

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# [(2*(n^2)+1] MUST be divisible by 3

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