Question

show that n²-n is divisinle
by 6.​

Answer 1

n² - n need to be always divisible by 6. The reason is that:

n²-n = n(n-1).

For the above value to be divisble by 6, either 'n' or (n-1), one of them must be equal to 3 or a mutiple of 3. But if you consider the entire integers, this is not always true.

Some examples where n²-n ≠ 6m, (m is a whole number).

5²-5 = 20, not divisibe by 6

8²-8 = 56, not divisible by 6 and so on.