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Hlaváček, Miloslav
On the set of solutions of the system $x\sb 1+x\sb 2+x\sb 3=1, x\sb 1x\sb 2x\sb 3=1$. (English). Mathematica Bohemica, vol. 123 (1998), issue 1, pp. 1-6
MSC: 10B05, 10M05, 11D04, 11D25, 11D72, 11G05 | MR 1618699 | Zbl 0898.11008 | DOI: 10.21136/MB.1998.126294
Keywords:
equations in many variables; linear diophantine equations; multiplicative equations; Weierstrass $p$-function; diophantine equations
Summary:
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.
References:
[1] K. Chandrasekharan: Elliptic Functions. Springer-Verlag, Berlin. Heidelberg, 1985. MR 0808396 | Zbl 0575.33001
[2] S. Schwarz: Algebraic Numbers. Přírodovědecké nakladatelství, Praha, 1950. (In Slovak.) MR 0048500
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