prove that n(n2-1) is div by 24...amazon puzzle

Question:

prove that n(n2-1) is div by 24

Note: n is odd and >=3

Solution:

N(N^2-1)=(N-1)N(N+1)
means it must be divisible by 2 and 3

since 24=2X2X2X3

so N(N^2-1) is divisible by 24.

for odd Ns,
(N-1) - is even, so div by 2 (smallest is 2)
N is odd
(N+1) - is even, next num div by 2 (smallest is 4=2x2)

N(N+1) is div by 3
So, 2x 2x2 x3 = 24 is a factor

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