Authors:
Gabriella Hajdu Institute of Mathematics and Computer Science, Faculty of Mechanical Engineering, Szent István University H-2103 Gödöllő, Páter K. u. 1., Hungary H-2103 Gödöllő, Páter K. u. 1., Hungary

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Lajos Hajdu Institute of Mathematics, University of Debrecen and the Number Theory Research Group of the Hungarian Academy of Sciences H-4010 Debrecen, P.O.B. 12, Hungary H-4010 Debrecen, P.O.B. 12, Hungary

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Summary  

We show that a well-known identity of Ramanujan admits only a bounded number of solutions over general finitely generated domains. The bound is explicit and uniform in the sense that it depends only on the dimensions of the domains involved. Our method is constructive, and opens up a possibility to determine the solutions in concrete instances. In some special cases all solutions are determined. Our results can also be considered as a continuation of some theorems of Z. Darczy and G. Hajdu, obtained over Z. We note that in case of Hossz's equation, similar results were obtained by several authors.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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