I saw somewhere that the sum of three consecutive squares minus $2$ is divisible by $3$. For example, $$2^2+3^2+4^2-2=4+9+16-2=27=3\cdot 9$$ But, I'm not sure how to give proof for this "property" of square. Can some one please show me how to do this or point me in right direction? I'm really not sure how to begin.
2026-04-11 20:13:13.1775938393
How prove this fact about consecutive square numbers?
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Hint
We have for any $n\in\mathbb Z,$ $(n-1)^2+n^2+(n+1)^2-2=...$
Work out the math and what do you notice?