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How does this imply $x = z^2$?
I read that given the equation:
$$
x + \frac{1}{x} = z^2 + \frac{1}{z^2}
$$
, we can imply that $x=z^2$.
But that $x=z^2$ is not obvious to me... I know we can match the variables on the left hand ...
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Mistake in the computation via partial fractions
This is a computation made in Titchmash's Introduction to Zeta functions. I was trying to reverse the computation. However, I kept missing factors.
Consider $\frac{1- xyz^2}{(1-z)(1-xz)(1-yz)(1-xyz)}...