K being any odd number greater than 1, k33 - k is always divisible by
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 24.
Consider k33 - k = k(k32 - 1) = k(k16 - 1)(k16 + 1)
= k(k8 - 1)(k8 + 1)(k16 + 1)
= k(k4 - 1)(k4 + 1)(k8 + 1)(k16 + 1)
= k(k2 - 1)(k2 + 1)(k8 + 1)(k8 + 1)(k16 + 1)
If k = 3, then k(k2 - 1) = 3 × 8 = 24
So, k33 - k is divisible by 24