Question

Show n^2 - n is a divisible by 3 for every positive n.

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Answer 1

: Let n be an even positive integer.

When n = 3q  

In this case , we have  

n2 - n = (3q)2 - 3q = 6q2 - 3q = 3q (2q - 1 )

n2 - n = 3r , where r = q (3q - 1)

n2 - n is divisible by 3.

Answer 2

Hence, ${n^2 - n}$ is divisible by 3, for every positive integer n.

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