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Prove this conjecture

Prove this conjecture-example-1
User Shadam
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1 Answer

1 vote

Answer:

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.