Thread: 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

Originally Posted by liedora

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 so that ?

Originally Posted by Drexel28

This doesn't make sense, isn't so that ?

Maybe I've got it wrong, but it looks like could be a set of integers. For example, , . Then, when , we have .

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