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Editorial
Can you prove that $1<\frac{xyz-1}{(x-1)(y-1)(z-1)}<\frac{x}{x-1}\frac{y}{y-1}\frac{z}{z-1}\leq2.\frac{3}{2}.\frac{4}{3}=4$ from the given information?
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Find the product of all $x+y+z$ for all the solutions $(x,y,z)$ such that $(x-1)(y-1)(z-1)$ is a divisor of $xyz-1$. Here, $x,y,z$ are integers and $1<x<y<z$.
Algebra
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