Question

Prove this conjecture

Answer 1

Answer:

See explanation

Step-by-step 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.