Question

for any positive integer n prove that n cube - n is divisible by 6​

Answer 1

Answer:

Case 2: Consider n = 2q + 1

Since, n (n – 1) (n + 1) is divisible by 2 and 3. Therefore, as per the divisibility rule of 6, the given number is divisible by six. n3 – n = n (n – 1) (n + 1) is divisible by 6.