Symmetric Equation I
C_K_Yang ironman353 liuguangxi zimpha a_forsteri guadruss C3PO Philippe_57721 sinan hervas benito255
Public  07/28/17  7xp  Programming  47.8% 
Here is the smallest known solution in positive integers for the Diophantine equation
$$ \frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y} = 4 $$
$x= 43736[\dots]772036 $
$y= 368751[\dots]055579 $
$z=1544768[\dots]277999 $
(The $\dots$ represent 70 digits !)
If we allow one variable to be negative, we can find smaller solutions.
For example, (x,y,z) = {1,4,11} and {5,9,11} are solutions of the above equation.
Find the first solution to
$ \frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y} = 38 \textrm{ with } x \lt 0 \lt y \lt z \textrm{ (coprime integers)}$
Answer format: x,y,z
[My timing: 15 sec]
$x= 43736[\dots]772036 $
$y= 368751[\dots]055579 $
$z=1544768[\dots]277999 $
(The $\dots$ represent 70 digits !)
If we allow one variable to be negative, we can find smaller solutions.
For example, (x,y,z) = {1,4,11} and {5,9,11} are solutions of the above equation.
Find the first solution to
$ \frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y} = 38 \textrm{ with } x \lt 0 \lt y \lt z \textrm{ (coprime integers)}$
Answer format: x,y,z
[My timing: 15 sec]
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