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2007 iTest Problems/Problem 46

Revision as of 23:01, 7 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let <math>(x,y,z)</math> be an ordered triplet of real numbers that satisfies the following system of equations: <cmath>\begin{align*}x+y^2+z^4&=0,\\y+z^2+x^4&=0,...")
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Problem

Let $(x,y,z)$ be an ordered triplet of real numbers that satisfies the following system of equations: \begin{align*}x+y^2+z^4&=0,\\y+z^2+x^4&=0,\\z+x^2+y^4&=0.\end{align*} If $m$ is the minimum possible value of $\lfloor x^3+y^3+z^3\rfloor$, find the modulo $2007$ residue of $m$.

Solution

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