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Folks this is How the legendary brilliant Kevincan analysed this problem

I think it is a good lesson to note

Enjoy

Both together

Either n=1, in which case n^2-1=0

or n is greater than from 1, in which case n-1 and n+1 are even and nonzero, because n is odd from (1). One of {n-1,n+1} will be a multiple of 2 and the other a multiple of 4, so (n-1)*(n+1) is divisible by 8.

Also, in three consecutive nonzero numbers, one will always be a multiple of 3. Since n is not a multiple of 3 (from (2)), either n-1 or n+1 is a multiple of 3 and so (n-1)*(n+1) is a multiple of 3 and thus of 24.

In either case, when n is divided by 24, the remainder is 0 SUFF