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Dense primitive polynomial sequences

Published online by Cambridge University Press:  26 February 2010

S. D. Cohen
S. D. Cohen
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow, G12 8QW.
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Extract

A sequence {an} of integers is said to be primitive if ai × aj whenever i ≠ j. Let f be a polynomial with integer coefficients and A a sequence of positive integers. We discuss further a problem considered in [1] in which I. Anderson, W. W. Stothers and the author investigated primitive sequences of the form f(A) = {f(x), x ∈ A}. (Of course, we can assume f(x)→ ∞ as x → ∞.) We shall prove the following theorem in which A(n), as usual, denotes the number of memhers of A that are. less than or equal to n.

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 89 - 91
Copyright
Copyright © University College London 1975

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References

1. Anderson, I., Cohen, S. D. and Stothers, W. W.. “Primitive polynomial subsequences”, Mathematika, 21 (1974), 239–247.CrossRefGoogle Scholar
2. Halberstam, H. and Roth, K. F.. Sequences, Vol. 1 (Oxford, 1966).Google Scholar