Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-24T06:35:21.944Z Has data issue: false hasContentIssue false

Simultaneous additive congruences to a large prime modulus

Published online by Cambridge University Press:  26 February 2010

O. D. Atkinson
Affiliation:
Department of Pure Mathematics, Hicks Building, Hounsfield Road, Sheffield. S3 7RH
J. Brüdern
Affiliation:
Mathematisches Institut, der Georg-August Universität, D-3400 Göttingen, Bunsenstrasse 3-5, Germany
R. J. Cook
Affiliation:
Department of Pure Mathematics, Hicks Building, Hounsfield Road, Sheffield. S3 7RH
Get access

Extract

Dörner [8] has recently proved a result for systems of additive equations over algebraic number fields, which we restate in a more specific setting.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Aigner, M.. Combinatorial Theory (Springer, 1979).Google Scholar
2.Atkinson, O. D., Brüdern, J. and Cook, R. J.. Three additive congruences to a large prime modulus. To appear in J. Austral. Math. Soc.Google Scholar
3.Atkinson, O. D. and Cook, R. J.. Pairs of additive congruences to a large prime modulus. J. Austral. Math. Soc., 46A (1989), 438455.CrossRefGoogle Scholar
4.Chowla, S., Mann, H. B. and Straus, E. G.. Some applications of the Cauchy-Davenport theorem. Kon. Norske Vidensk. Selsk. Fork., 32 (1959), 7480.Google Scholar
5.Davenport, H.. Analytic Methods for Diophantine Equations and Diophantine Inequalities (Campus Publishers, Ann Arbor, 1963).Google Scholar
6.Davenport, H. and Lewis, D. J.. Simultaneous equations of additive type. Phil. Trans. Roy. Soc London, 264A (1969), 557595.Google Scholar
7.Dodson, M. M.. Homogeneous additive congruences. Phil. Trans. Roy. Soc. London, 261A (1966), 163210.Google Scholar
8.Dörner, E.. Simultaneous diagonal equations over certain p-adic fields. J Number Theory, 36 (1990), 111.Google Scholar
9.Low, L., Pitman, J. and Wolff, A.. Simultaneous diagonal congruences. J. Number Theory, 19 (1988), 3159.CrossRefGoogle Scholar
10.Schmidt, W. M.. Equations over Finite Fields, An Elementary Approach, Lecture Notes in Mathematics 536 (Springer, 1976).CrossRefGoogle Scholar
11.Schmidt, W. M.. The solubility of certain p-adic equations. J. Number Theory, 19 (1984), 6380.CrossRefGoogle Scholar
12.Wooley, T. D.. On simultaneous additive equations III. Mathematika, 37 (1990), 8596.Google Scholar