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Find all integers x for which there exists an integer y such that 1/x + 1/y = \(\frac{1}{17}\)

 Feb 1, 2022
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\(\frac{1}{x} + \frac{1}{y} = \frac{1}{17}\)

\(\frac{x + y}{xy} = \frac{1}{17}\)

\(17(x + y) = xy\)

\(0 = xy - 17x - 17y\)

\(289 = (x - 17)(y - 17)\)

 

x-17 y-17 x y
1 289 18 306
17 17 34 34
289 1 306 18
       

 

The possible values of x are 18, 34, and 306.

 Feb 1, 2022

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