1/x + 1/y = 1/z, (x, z) = 1

 
 
Let   x, \; y, \; z   be positive integer for which

1/x \; + \; 1/y \; = \; 1/z,         (x, z) \; = \; 1

Prove that    x+y,    x-z    and    y-z    are all squares

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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