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Acta Mathematica Hungarica
Authors:
Gabriella Hajdu
and
Lajos Hajdu
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.
