Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-09T05:18:49.309Z Has data issue: false hasContentIssue false
  • English
  • Français

On representing integers as products of integers of a prescribed type

Published online by Cambridge University Press:  09 April 2009

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
Department of MathematicsUniversity of CloardoBoulder, Colorado 80309, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A general group-theoretic procedure is indicated for representing rational integers as products of other integers. A detailed example is given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 143 - 161
Copyright
Copyright © Australian Mathematical Society 1983

References

Burgess, D. A. (1962), ‘On character sums and primitive roots’, Proc. London Math. Soc. 12, 179–192.CrossRefGoogle Scholar
Burgess, D. A. (1967), ‘On the quadratic character of a polynomial’, J. London Math. Soc. 42, 73–80.CrossRefGoogle Scholar
Davenport, H. (1963), ‘Cubic forms in 16 variables’, Proc. Roy. Soc. Ser. A 272, 285–303.Google Scholar
Dress, F. and Volkmann, B., ‘Ensembles d'unicité pour les fonctions arithmétiques additives ou multiplicatives’, C. R. Acad. Sci. Paris Ser. A 287, 43–46.Google Scholar
Elliott, P. D. T. A. (1979/1980), Probabilistic number theory I, II (Springer, New York, Heidelberg, Berlin).CrossRefGoogle Scholar
Elliott, P. D. T. A. (1974), ‘A conjecture of Kátai’, Acta Arith. 26, 11–20.CrossRefGoogle Scholar
Elliott, P. D. T. A. (1976), ‘On two conjectures of Kátai’, Acta Arith. 30, 35–59.CrossRefGoogle Scholar
Kaplansky, I. (1969), Infinite abelian groups, revised edition (University of Michigan Press, Ann Arbor).Google Scholar
Kátai, I. (1968a), ‘On sets characterising number-theoretical functions’, Acta Arith. 13 315–320.CrossRefGoogle Scholar
Kátai, I. (1968b), ‘On sets characterising number-theoretical functions (II), (The set of “prime plus one” s is a set of quasi-uniqueness)’, Acta Arith. 16, 1–4.CrossRefGoogle Scholar
Vaughan, R. C. (1981), The Hardy Littlewood method (Cambridge University Tract No. 80).Google Scholar
van der Waerden, B. (1953), Modern algebra (Ungar, New York, 1931).Google Scholar
Wirsing, E. (1980), ‘Additive functions with restrictive growth on the numbers of the form p + 1’, Acta Arith. 37, 345–357.CrossRefGoogle Scholar
Wolke, D. (1978), ‘Bemerkungen über Eindeutigkeitsmengen additiver Funktionen’, Elem. Math. 33, 14–16.Google Scholar
Zariski, O. and Samuel, P., Commutative algebra (Van Nostrand, Toronto, London, New York, 1958).Google Scholar