Multiple choice

What is the largest number by which the expression n3 - n is divisible for all possible integral values of n?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 6
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

n3 - n = (n - 1) (n) (n + 1), for integral values of n, represents the product of three consecutive integers. Since in a pair of consecutive integers, there is a multiple of two and in a triplet of consecutive integers, there is a multiple of three, then n3 - n is divisible by 6. Hence, option (5) is the correct option.

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