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Romania District Olympiad 2001 - VIII Grade

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March 12, 2011
number theory proposednumber theory

Problem Statement

Let x,y,z∈R∗x,y,z\in \mathbb{R}^* such that xy,yz,zx∈Qxy,yz,zx\in \mathbb{Q}.
a) Prove that x2+y2+z2x^2+y^2+z^2 is rational; b) If x3+y3+z3x^3+y^3+z^3 is rational, prove that x,y,zx,y,z are rational.
Marius Ghergu
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