Is every natural number a difference between natural numbers with greatest common divisor 1.

Can one prove that $\{x : x=y-z, \gcd(y,z)=1, y,z\in \mathbb{N}\}=\mathbb{N}$?

This problem has arisen at a problem in probability and I've never studied this kind of math before, so I apologize if it is tagged wrong.

Thanks

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$x= (x+1)-1$. Or if you don't want to use $z=1$ take any number $m$ that is coprime to $x$ and use $x=(x+m)-m$. –  Michalis Nov 3 '12 at 12:06
Let $n$ be an integer bigger than $6$. Then $n$ is the sum of two relatively prime integers each bigger than $1$. –  PAD Nov 3 '12 at 14:35

Try $x=(x+1)-1$.