Prove that all integers are of the form 3k, 3k+1, or 3k+2

The problem is clearly easy and it's obvious why this is true, but I just don't understand how exactly to go about proving it...help?

Thanks!

Printable View

- February 5th 2010, 06:21 AMeliss93Prove that all integers are of the form...
Prove that all integers are of the form 3k, 3k+1, or 3k+2

The problem is clearly easy and it's obvious why this is true, but I just don't understand how exactly to go about proving it...help?

Thanks! - February 5th 2010, 06:36 AMhavaliza
Because the reminder of division any number by 3 is 0, 1 or 2. so is or or

- February 5th 2010, 06:37 AMBlack
Follows from the division algorithm (using an integer and 3). For each integer , there exists unique integers and such that

, where .