# For all $d\in \mathbb N$ exists two numbers $a,b\in\mathbb Z$ such that $\text{gcd}(a,b)=d$?

This is maybe a stupid question but I have to ask,

Is it correct that for all $d\in \mathbb N$ exists two numbers $a,b\in\mathbb Z$ such that $\text{gcd}(a,b)=d$?

I think that the answer is NO e.g let's take $d=0$

Am I correct?

• Is $0$ a natural number? – Igor Rivin Mar 5 '16 at 20:57
• Yes it is, why not? – Error 404 Mar 5 '16 at 20:59
• @Error404 : Ok, Is it true for non zero natural numbers? – user312648 Mar 5 '16 at 21:00
• For non zero I think that the answer will be Yes – Error 404 Mar 5 '16 at 21:01
• Some authors will assume $\mathbb{N}$ not to include $0$, so it's best to make this explicit. – Fryie Mar 5 '16 at 21:08

You are correct if $0 \in \Bbb N$ For all other numbers, there are.