Discussiones Mathematicae General Algebra and Applications 20(2) (2000) 193-198
doi: 10.7151/dmgaa.1016

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SOME CLASSES OF DIOPHANTINE EQUATIONS CONNECTED WITH McFARLAND'S AND MA'S CONJECTURES

Zhenfu Cao

Department of Mathematics, Harbin Institute of Technology
Harbin 150001, P. R. China
e-mail: zfcao@hope.hit.edu.cn

Aleksander Grytczuk

Institute of Mathematics, Kotarbiński Pedagogical University
pl. Słowiański 6, 65-069 Zielona Góra, Poland
e-mail: agryt@lord.wsp.zgora.pl

Abstract

In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.

Keywords: difference sets, diophantine equations, Pell's equations.

1991 Mathematics Subject Classification: 11D09, 05B10.

References

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Received 11 March 1998
Revised 24 October 2000
Revised 4 December 2000