Some classes of Diophantine equations connected with McFarland's and Ma's conjectures

• Autorzy: Zhenfu Cao , Aleksander Grytczuk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

difference sets; diophantine equations; Pell's equations

Kategorie tematyczne

• 05B10: Difference sets (number-theoretic, group-theoretic, etc.)
• 11D09: Quadratic and bilinear equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 193-198

Daty

wydano

2000

otrzymano

1998-03-11

poprawiono

1999-10-24

poprawiono

1999-12-04

Twórcy

autor

Zhenfu Cao

• Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China

autor

Aleksander Grytczuk

• Institute of Mathematics, Kotarbiński Pedagogical University, pl. Słowiański 6, 65-069 Zielona Góra, Poland

Bibliografia

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• [3] Z. Cao, 'Introduction to Diophantine equations' (Chinese), Harbin Inst. of Technology Press, Harbin 1989.
• [4] Z. Cao, On the equation $ax^{m}-by^{n} = 2$, Chinese Sci. Bull. 35 (1990), 1227-1228.
• [5] Z. Cao, On the Diophantine equation $(ax^{m}-4c)/(abx-4c) = by²$ (Chinese), J. Harbin Inst. Tech. 23 (1991), suppl, 110-112.
• [6] G. Degert, Über die Bestimung der Grundeinheit gewisser reell-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 22 (1958), 92-97.
• [7] Y.-D. Guo, On the exponential Diophantine equation $x² = 2^{2a}k^{2m} - 2^{2a}k^{m+n} + 1$, Discuss. Math.- Algebra & Stochastic Methods 16 (1996), 57-60.
• [8] S.L. Ma, McFarland's conjecture on abelian difference sets with multiplier -1, Des. Codes Cryptogr. 1 (1992), 321-332.
• [9] L.J. Mordell, 'Diophantine Eqations', Academic Press, London 1969.
• [10] C. Richaud, Sur la résolution des équations x² - Ay² = ±, Atti Acad. Pontif. Nuovi Lincei, 1866, 177-182.
• [11] C. Strømer, Quelques theorems sur l'equation de Pell x² - Dy² = ±1 et leur applications, Skr. Norske Vid. Acad., I Selsk. Mat. Natur. Kl., No. 2 (1897), 48 pp.

Identyfikatory

DOI

10.7151/dmgaa.1016