# Inspired by a NT problem from BMO

Number Theory Level pending

If $$n$$ is a positive integer greater than 6 and 720 divides $$n^2 (n^2+16)$$ then sum of all possible remainders (not necessarily distinct) obtained on dividing $$n+1$$ and $$n-1$$ by 2, 3, 5 will be equal to $$\text{___________}$$.

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