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

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Published:2004-09-01
Printed: Sep 2004
• Kevin Ford
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Abstract

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.
 MSC Classifications: 11A05 - Multiplicative structure; Euclidean algorithm; greatest common divisors

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