Integral Solutions of Markov-Hurwitz Equations

✍ Scribed by A. Baragar

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 488 KB
• Volume: 49
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1994.1078

✦ Synopsis

In this paper, a characterization for all pairs ((a, n)) with (a \geqslant 2(n-1)^{1 / 2}) for which the equation (M_{a, n}: x_{1}^{2}+\cdots+x_{n}^{2}=a x_{1} \cdots x_{n}) has positive integral solutions is given. It is known that for any pair ((a, n)), the integral solutions of (M_{a, n}) can be expressed as orbits of a finite set of fundamental solutions under the action of a group of automorphisms. Also presented in this paper are two very different constructions that yield sequences of equations whose sets of fundamental solutions grow without bound. C 1994 Academic Press, Inc.