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
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?