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Sets of integers containing no n terms in geometric progression

Published online by Cambridge University Press:  18 May 2009

J. Riddell
J. Riddell
Affiliation:
University of VictoriaVictoria, B.C., Canada
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R. A. Rankin [3] considered the problem of finding, for each integer n ≧ 3, a sequence of positive integers containing no n−term geometric progression. He constructed such sets Bn having asymptotic density

For example A3 ≑ 0·71975, A4 ≑ 0·8626, and An→1 as n → ∞.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 2 , July 1969 , pp. 137 - 146
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

1.Ayoub, R., An introduction to the analytic theory of numbers, Mathematical Surveys, No. 10. American Mathematical Society (Providence, 1963), p. 86.Google Scholar
2.Bateman, P. T., Solution to Problem 4459 [1951, p. 636], American Math. Monthly 61 (1954), 477–479.Google Scholar
3.Rankin, R. A., Sets of integers containing not more than a given number of terms in arithmetical progression, Proc. Roy. Soc. Edinburgh Sect. A 65 (1962), 332–344.Google Scholar