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Method of Finding LCM

For any posit...

Question

Question 4
For any positive integer n, prove that $n^{3} - n$ is divisible by 6.

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Solution

Let $a = n^{3} - n$
$= n (n^{2} - 1) = n (n + 1) (n - 1)$
This is the product of three consecutive positive integers. We know that the product of three consecutive positive integers is divisible by 2 as well as 3. So, it must be divisible by 6.

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Q. Question 4
For any positive integer n, prove that

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For any positive integers n, prove that $n^{3} - n$ is divisible by 6.

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Method of Finding LCM

Standard X Mathematics

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