SOLUTION: Prove the following conjecture: "The sum of any three positive consecutive odd integers will be divisible by three." This is urgent! Thank you!

SOLUTION: Prove the following conjecture: "The sum of any three positive consecutive odd integers will be divisible by three." This is urgent! Thank you!

Algebra.Com

Question 310154: Prove the following conjecture:
"The sum of any three positive consecutive odd integers will be divisible by three."
This is urgent! Thank you!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The sum is
n + n+2 + n+4
= 3n+6 which is divisible by 3.
----------------------
The sum of any 3 consecutive integers is divisible by 3, odd, even, negative, doesn't matter.
RELATED QUESTIONS
Prove the following conjecture: "The sum of any three positive consecutive integers will (answered by scott8148)

Prove that the product of three consecutive positive integers is divisible by... (answered by CubeyThePenguin)

Prove that the sum of the cubes of any two consecutive odd integers is divisible by... (answered by Edwin McCravy,math_tutor2020)

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

Conjecture: The sum of three consecutive integers is always three times... (answered by solver91311)

Prove the conjecture below by writing a variable statement and using algebra.... (answered by Fombitz)

Prove the conjecture below by writing a variable statement and using algebra.... (answered by KMST)

Show that 1 greater than the sum of the squares of any three consecutive integers is... (answered by richard1234)

prove that the product of any three consecutive numbers is even. So far I have tried , (answered by josgarithmetic,tenkun,amalm06,ikleyn)