Question

Prove this conjecture

Answer 1

See explanation

Explanation:

Consider the natural number
`n(n+1)(n+2).`

If
`n` is the natural number, then
`n+1, \ n+2` are next two natural numbers, so numbers
`n,\ n+1` and
`n+2` are three consecutive numbers.

Given three consecutive natural numbers, one of them is always even number and one of them is always multiple of 3, so the product

`n(n+1)(n+2)`

is divisible by 6.