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A Strong Form of a Problem of R. L. Graham

Published online by Cambridge University Press:  20 November 2018

Kevin Ford
Kevin Ford*
Affiliation:
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801 USA, e-mail: [email protected]
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Abstract

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If $A$ is a set of $M$ positive integers, let $G(A)$ be the maximum of ${{a}_{i}}/\,\gcd ({{a}_{i}},\,\,{{a}_{j}}\,)$ over ${{a}_{i}},\,{{a}_{j}}\,\,\in \,\,A.$ We show that if $G(A)$ is not too much larger than $M$, then $A$ must have a special structure.

Keywords

11A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 358 - 368
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Balasubramanian, R. and Soundararajan, K., On a conjecture of R. L. Graham. Acta Arith. 75 (1996), 1–38.Google Scholar
[2] Ford, K., Maximal collections of intersecting arithmetic progressions. Combinatorica 23 (2003), 263–281.Google Scholar
[3] Graham, R. L., Advanced Problem 5749. Amer.Math. Monthly 77(1970), 775.Google Scholar
[4] Szegedy, M., The solution of Graham's greatest common divisor problem. Combinatorica 6 (1986), 67–71.Google Scholar
[5] Zaharescu, A., On a conjecture of Graham, J. Number Theory 27 (1987), 33–40.Google Scholar