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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