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Given that $x$, $\frac{1}{x}$, $y$, $\frac{1}{y}$, $z$ and $\frac{1}{z}$ are all integers, how many distinct values of $x+ y+ z$ are possible?

 Feb 17, 2021
 #1
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I think x y and z can each be  1  or -1  

 

1 + 1 +1 = 3

-1 + 1 +1  =1

-1 -1 + 1  = -1

-1 -1 -1   = -3         4 values

 Feb 17, 2021

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