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Math Help - Little proof

  1. #1
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    Little proof

    Hi I was wondering if I could get some help with the following proof.

    Let x,d be integers where d>0. Prove that the intersection of M and the natural numbers is non empty where M={x-qd | q is integer}

    Cheers
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Little proof

    Quote Originally Posted by liedora View Post
    Hi I was wondering if I could get some help with the following proof.

    Let x,d be integers where d>0. Prove that the intersection of M and the natural numbers is non empty where M={x-qd | q is integer}

    Cheers
    This doesn't make sense, isn't M\subseteq\mathbb{N} so that M\cap\mathbb{N}=M\ne\varnothing?
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  3. #3
    Senior Member roninpro's Avatar
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    Re: Little proof

    Quote Originally Posted by Drexel28 View Post
    This doesn't make sense, isn't M\subseteq\mathbb{N} so that M\cap\mathbb{N}=M\ne\varnothing?
    Maybe I've got it wrong, but it looks like M could be a set of integers. For example, x=10, d=7. Then, when q=2, we have 10-2\cdot 7=-4.

    ----

    In regards to the original question, you are basically asked to show that the set M has at least one positive number in it. The way to go about this is to explicitly produce one. Suppose x is positive. Can you find something positive in M? What if x is negative?
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