Question

for any positive integer n , prove that n^3 - n is divisible by 6
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Answer 1

Step-by-step explanation:

Put x=3

Given equation= n^3-n

p(3)= (3)^3-3

=27-3

=24

we have to prove that the result is divisible by 6:-

=24/6

=4

Hence, proved.

Hope this may help you

Answer 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

Step-by-step explanation:

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