Thread: division question

Let x, y, d, be elements of Z (integers) and let z = x+y. Prove: If d divides any two of x, y, z then d divides the third.

How do you prove this? I know it's true, but not how to prove it.

Originally Posted by vassago

Let x, y, d, be elements of Z (integers) and let z = x+y. Prove: If d divides any two of x, y, z then d divides the third.

How do you prove this? I know it's true, but not how to prove it.

Suppose that and

Now sub into the above equation and you get