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Math Help - division question

  1. #1
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    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.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by vassago View Post
    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 d|x \implies x=q_1d and d|y \implies y=q_2d

    Now sub into the above equation and you get

    z=q_1d+q_2d \iff z=(q_1+q_2)d \implies d|z
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