Question

for any positive integer n,prove that n²-n is divisible by 6?​

Answer 1

Answer:

Let us consider

a = n³ – n

a = n (n² – 1)

a = n (n + 1)(n – 1)

Assumtions:

1. Out of three (n – 1), n, (n + 1) one must be even, so a is divisible by 2.

2. (n – 1) , n, (n + 1) are consecutive integers thus as proved a must be divisible by 3.

From (1) and (2) a must be divisible by 2 × 3 = 6

Thus, n³ – n is divisible by 6 for any positive integer n.

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Hope it helps you!!

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Answer 2

Answer:

let us keep the positive integer n as 10

10^2-10=10×10-10=90 omg it is not divisible by 6 .sorry I don't know