Question

prove that one of any three consecutive positive integers must be divisible by 3

Answer 1

The numbers in the table of three comes after every two number e.g.3 then leaving 4 and 5 comes 6 and so on....so picking any 3 numbers will always give you a number in them which is divisible by 3 (sorry that's the best thought uptil now that I got...so this is probably not the perfect solution.)

Answer 2

Step-by-step explanation:

Let 3 consecutive positive integers be n, n + 1 and n + 2 .

Whenever a number is divided by 3, the remainder we get is either 0, or 1, or 2.

:

Therefore:

n = 3p or 3p+1 or 3p+2, where p is some integer

If n = 3p = 3(p) , then n is divisible by 3

If n = 3p + 1, then n + 2 = 3p +1 + 2 = 3 p + 3 = 3 ( p + 1 ) is divisible by 3

If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3

Thus, we can state that one of the numbers among n, n+1 and n+2 is always divisible by 3

Hence it is solved.