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Assume all variables are integers greater than 1.

Suppose $y = k x$ and $k \neq x$. Suppose that $z\lt k$ and $\gcd(k, z) \gt 1$.

Does this imply $\gcd(z, x) \lt x$?

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@Arturo Magidin Thanks for the edit. – Tom Tucker Feb 11 '12 at 3:28
up vote 3 down vote accepted

No. Take for example $k=8$, $x=2$, and $z=4$.

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