Find an integral non-trivial solution (x,y,z ~=0) (x=0 or y=0 or z=0 are trivial) for the cubic equation
987,654,321x + 123,456,789y + z = (x+y+z)^3.
Provide solution with minimum Positive value of (x+y+z). The solution does not require x,y,or z to be positive.
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One method: meshgrid
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Solution 1216892
The solution (or actually one of many solutions) of this cubic equation with minimal integer positive value of (x+y+z), is x = 30,864,197 , y = -246,913,580 , z = 216,049,384 ; in that case, x+y+z = 1, and you can't get smaller than that. (Sorry, I wrote the same thing as a remark in the solution script, but I made a typo and wrote the wrong value of z there.)