Question

for any positive integer n prove that n3_n is divisible by 6 (or) show that the product of any three consecutive positive integer is always divisible by 6​

Answer 1

Answer:

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. Thus, n³ – n is divisible by 6 for any positive integer n.