SOLUTION: Prove the following conjecture: "The sum of any three positive consecutive integers will be divisible by three" urgent thank you!

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Prove the following conjecture: "The sum of any three positive consecutive integers will be divisible by three" urgent thank you!      Log On


   

Question 310155: Prove the following conjecture:
"The sum of any three positive consecutive integers will be divisible by three"
urgent thank you!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let n=1st integer, so (n+1)=2nd integer and (n+2)=3rd integer

sum of integers ___ n + n+1 + n+2 = 3n+3

dividing the sum by 3 ___ (3n+3) / 3 = n+1

the sum is divisible by 3 and the result is the 2nd integer