1. ## 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

2. ## Re: Little proof

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 $M\subseteq\mathbb{N}$ so that $M\cap\mathbb{N}=M\ne\varnothing$?

3. ## Re: Little proof

Originally Posted by Drexel28
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 $10-2\cdot 7=-4$.

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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?