SOLUTION: Prove that the product of three consecutive positive integers is divisible by 6.

SOLUTION: Prove that the product of three consecutive positive integers is divisible by 6.

Algebra.Com

Question 969707: Prove that the product of three consecutive positive integers
is divisible by 6.
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
n(n+1)(n+2)

Out of these numbers, at least one of them is even and at least one of them is a multiple of 3.

even:
even, odd, even
odd, even, odd

divisible by 3 (use remainders):
0, 1, 2
1, 2, 0
2, 0, 1

Therefore, the product of any three consecutive integers is divisible by 6.
RELATED QUESTIONS
Prove that the product of three consecutive integers is divisible by 6; of four... (answered by Edwin McCravy)

Prove that one of every three consecutive positive numbers is divisible by 3 (answered by addingup)

Prove the following conjecture: "The sum of any three positive consecutive integers will (answered by scott8148)

Prove the following conjecture: "The sum of any three positive consecutive odd integers... (answered by Alan3354)

"Show that the product of three consecutive natural numbers is divisible by... (answered by richard1234)

why is the product of 3 consecutive integers divisible by 6 (answered by richard1234)

The product of two consecutive positive integers is always divisible by an integer... (answered by Greenfinch)

The product of two consecutive positive integers is always divisible by an integer... (answered by Alan3354)

I'm really sorry, I don't study maths in English so I really have no idea where to put... (answered by CubeyThePenguin,ikleyn)