Geodesic
On the set of solutions of the system $x\sb 1+x\sb 2+x\sb 3=1, x\sb 1x\sb 2x\sb 3=1$
Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 1-6

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MR Zbl
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.
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.
DOI : 10.21136/MB.1998.126294
Classification : 10B05, 10M05, 11D04, 11D25, 11D72, 11G05
Keywords: equations in many variables; linear diophantine equations; multiplicative equations; Weierstrass $p$-function; diophantine equations 
Hlaváček, Miloslav. On the set of solutions of the system $x\sb 1+x\sb 2+x\sb 3=1, x\sb 1x\sb 2x\sb 3=1$. Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 1-6. doi: 10.21136/MB.1998.126294
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[1] K. Chandrasekharan: Elliptic Functions. Springer-Verlag, Berlin. Heidelberg, 1985. | MR | Zbl

[2] S. Schwarz: Algebraic Numbers. Přírodovědecké nakladatelství, Praha, 1950. (In Slovak.) | MR

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