Math, asked by Iamwhoiamho, 1 month ago

Q- Prove that some of square of two odd positive


Q- Show that for any positive integer n, n³-n is divisible by 6



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Answers

Answered by hridayeshdas2007
2

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.

Answered by IIYourFirstDeathII
6

Answer:

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Step-by-step explanation:

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