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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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    Let $n$ be an integer bigger than $6$. Then $n$ is the sum of two relatively prime integers each bigger than $1$.2012-11-03

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

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    Oh wow, that was trivial. Thanks!2012-11-03