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?

  • $\begingroup$ Is $0$ a natural number? $\endgroup$ – Igor Rivin Mar 5 '16 at 20:57
  • $\begingroup$ Yes it is, why not? $\endgroup$ – Error 404 Mar 5 '16 at 20:59
  • $\begingroup$ @Error404 : Ok, Is it true for non zero natural numbers? $\endgroup$ – user312648 Mar 5 '16 at 21:00
  • $\begingroup$ For non zero I think that the answer will be Yes $\endgroup$ – Error 404 Mar 5 '16 at 21:01
  • 1
    $\begingroup$ Some authors will assume $\mathbb{N}$ not to include $0$, so it's best to make this explicit. $\endgroup$ – Fryie Mar 5 '16 at 21:08

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


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