| Title:
|
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) |
| Author:
|
Hlaváček, Miloslav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
1-6 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
equations in many variables |
| Keyword:
|
linear diophantine equations |
| Keyword:
|
multiplicative equations |
| Keyword:
|
Weierstrass $p$-function |
| Keyword:
|
diophantine equations |
| MSC:
|
10B05 |
| MSC:
|
10M05 |
| MSC:
|
11D04 |
| MSC:
|
11D25 |
| MSC:
|
11D72 |
| MSC:
|
11G05 |
| idZBL:
|
Zbl 0898.11008 |
| idMR:
|
MR1618699 |
| DOI:
|
10.21136/MB.1998.126294 |
| . |
| Date available:
|
2009-09-24T21:28:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126294 |
| . |
| Reference:
|
[1] K. Chandrasekharan: Elliptic Functions.Springer-Verlag, Berlin. Heidelberg, 1985. Zbl 0575.33001, MR 0808396 |
| Reference:
|
[2] S. Schwarz: Algebraic Numbers.Přírodovědecké nakladatelství, Praha, 1950. (In Slovak.) MR 0048500 |
| . |
