# finding all pairs $(x,z)$

How to find all pairs $(x,z)$ of integers for which $2(z+1)^3$ is divisible by $xz-1$

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Have you tried compiling numerous examples and searching them for patterns? – Gerry Myerson Oct 26 '12 at 6:32

Here's all the pairs of $(x,z)$ I could find for positive $x,z$. On the right is $2(z+1)^3/(xz-1)$