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

Zhenfu Cao; Aleksander Grytczuk

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 193-198
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Zhenfu Cao, and Aleksander Grytczuk. "Some classes of Diophantine equations connected with McFarland's and Ma's conjectures." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 193-198. <http://eudml.org/doc/287675>.

@article{ZhenfuCao2000,
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.},
author = {Zhenfu Cao, Aleksander Grytczuk},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {difference sets; diophantine equations; Pell's equations},
language = {eng},
number = {2},
pages = {193-198},
title = {Some classes of Diophantine equations connected with McFarland's and Ma's conjectures},
url = {http://eudml.org/doc/287675},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Zhenfu Cao
AU - Aleksander Grytczuk
TI - Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 193
EP - 198
AB - 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.
LA - eng
KW - difference sets; diophantine equations; Pell's equations
UR - http://eudml.org/doc/287675
ER -

References

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  1. [1] K.T. Arasu, Recent results on difference sets, 'Coding Theory and Design Theory', Part II, Springer-Verlag, Berlin-New York 1990, 1-23. Zbl0747.05013
  2. [2] Z. Cao, Some Diophantine equations in difference sets, a lecture, '5-th National Combinatorial Mathematics Conference', Shanghai 1994. 
  3. [3] Z. Cao, 'Introduction to Diophantine equations' (Chinese), Harbin Inst. of Technology Press, Harbin 1989. 
  4. [4] Z. Cao, On the equation a x m - b y n = 2 , Chinese Sci. Bull. 35 (1990), 1227-1228. 
  5. [5] Z. Cao, On the Diophantine equation ( a x m - 4 c ) / ( a b x - 4 c ) = b y ² (Chinese), J. Harbin Inst. Tech. 23 (1991), suppl, 110-112. Zbl0971.11518
  6. [6] G. Degert, Über die Bestimung der Grundeinheit gewisser reell-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 22 (1958), 92-97. Zbl0079.05803
  7. [7] Y.-D. Guo, On the exponential Diophantine equation x ² = 2 2 a k 2 m - 2 2 a k m + n + 1 , Discuss. Math.- Algebra Stochastic Methods 16 (1996), 57-60. 
  8. [8] S.L. Ma, McFarland's conjecture on abelian difference sets with multiplier -1, Des. Codes Cryptogr. 1 (1992), 321-332. Zbl0758.05028
  9. [9] L.J. Mordell, 'Diophantine Eqations', Academic Press, London 1969. 
  10. [10] C. Richaud, Sur la résolution des équations x² - Ay² = ±, Atti Acad. Pontif. Nuovi Lincei, 1866, 177-182. 
  11. [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. 

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