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The simultaneous representation of integers by products of certain rational functions

Published online by Cambridge University Press:  09 April 2009

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
University of ColoradoBoulder, Colorado 80309, U.S.A.
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Abstract

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It is proved that an arbitrary pair of positive integers can be simultaneously represented by products of the values at integer points of certain rational functions. Linear recurrences in Z-modules and elliptic power sums are applied.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 405 - 420
Copyright
Copyright © Australian Mathematical Society 1983

References

Cassels, J. W. S. (1957), An introduction to diophantine approximation (Cambridge University Tracts No. 45).Google Scholar
Elliott, P. D. T. A. (1979a), ‘Sums and differences of additive arithmetic functions in mean square,’ J. Reine Angew. Math. 309, 21–54.Google Scholar
Elliott, P. D. T. A. (1979b), Probabilistic number theory, I (Grundlehren Math. Wiss. No. 239, Springer, Berlin and New York).CrossRefGoogle Scholar
Elliott, P. D. T. A. (1980), ‘On sums of additive arithmetic functions with shifted arguments,’ J. London Math. Soc. (2) 22, 25–38.CrossRefGoogle Scholar
Elliott, P. D. T. A. (1983), ‘On representing integers as products of integers of a prescribed type,’ J. A ustral. Math. Soc. Ser A 35, 143–161.CrossRefGoogle Scholar
Halberstam, H. and Richert, H.E. (1974), Sieve methods (Academic Press, London).Google Scholar
Vaughan, R. C. (1981), The Hardy-Littlewood method (Cambridge University Tracts No. 80).Google Scholar