MATHEMATICA BOHEMICA, Vol. 123, No. 1, pp. 1-6, 1998

On the set of solutions of the system
$x_1+x_2+x_3 = 1$, $x_1x_2x_3=1$

Miloslav Hlavacek

Ivan Hlavacek, Matematicky ustav AV CR, Zitna 25, 115 67 Praha 1, Czech Republic

Abstract: A proof is given that the system in the title has infinitely many solutions of the form $a_1 + \ii a_2$, where $a_1$ and $a_2$ are rational numbers.

Keywords: Diophantine equations, Weierstrass $p$-function

Classification (MSC 1991): 10B05, 10M05

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