#1**+1 **

*prove:*

*n^3-n is divisible by 3*

n^{3} – n

Factor out an n (n) • (n^{2} – 1)

Factor n^{2} – 1 (n) • (n + 1) • (n – 1)

Rearrange terms (n – 1) • (n) • (n + 1)

Note that the expression consists of three consecutive integers.

When you have three consecutive integers, one of them will be divisible by 3.

If one of the multipliers is divisible by three, then the product is divisible by 3.

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Guest Sep 8, 2020