Problem 629. Cubic Integer Constrained Solution

Created by Richard Zapor

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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.

Question courtesy of The Contest Center

One method: meshgrid

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Last solution submitted on Apr 02, 2019

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1 Comment

yurenchu on 20 Jun 2017

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.)

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Problem 629. Cubic Integer Constrained Solution

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Problem 629. Cubic Integer Constrained Solution

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Last 200 Solutions

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