Prove or disprove using a counterexample ......?

Question

Prove or disprove using a counterexample that the sum of any three consecutive even integers is divisible by 6.

Answer 1

If the middle number is n, the others are n-2 and n + 2, so that their sum is S = n-2 + n + n+2 = 3n. But since n is even, n= 2n' for some integer n', and their sum S is given by S = 3 * 2n' = 6 n'. Therefore, S is divisible by 6.

Answer 2

If we call the first of the 3 integers 2N, then the second and third integers are 2N+2 and 2N+4.

The sum of the three integers is 2N + (2N+2) + (2N+4)
= 6N+6

6N+6 = 6(N+1) is obviosly divisible by 6...

Answer 3

Why can't you use a counterexample? That's exactly how you would prove this false (which it is). Look, 5|(2+3), but 5 doesn't divide 2 or 3.

Answer 4

This is true.

Three consecutive even integers will have the form 2k, 2k + 2, 2k + 4, for some integer k.

If I add these together, I get 6k + 6, which is certainly divisible by 6.

Answer 5

-2, 0, 2

Answer 6

2x+2x+2+2x+4=6x+6
Please give me best answer thanks!