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 $\displaystyle M$ could be a set of integers. For example, $\displaystyle x=10$, $\displaystyle d=7$. Then, when $\displaystyle q=2$, we have $\displaystyle 10-2\cdot 7=-4$.
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In regards to the original question, you are basically asked to show that the set $\displaystyle M$ has at least one positive number in it. The way to go about this is to explicitly produce one. Suppose $\displaystyle x$ is positive. Can you find something positive in $\displaystyle M$? What if $\displaystyle x$ is negative?