Geodesic
A Strong Form of a Problem of R. L. Graham
Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 358-368

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2004-035-7
Mots-clés : 11A05 
Ford, Kevin. A Strong Form of a Problem of R. L. Graham. Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 358-368. doi: 10.4153/CMB-2004-035-7
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[1] [1] Balasubramanian, R. and Soundararajan, K., On a conjecture of R. L. Graham. Acta Arith. 75 (1996), 1–38. Google Scholar

[2] [2] Ford, K., Maximal collections of intersecting arithmetic progressions. Combinatorica 23 (2003), 263–281. Google Scholar

[3] [3] Graham, R. L., Advanced Problem 5749. Amer.Math. Monthly 77(1970), 775. Google Scholar

[4] [4] Szegedy, M., The solution of Graham's greatest common divisor problem. Combinatorica 6 (1986), 67–71. Google Scholar

[5] [5] Zaharescu, A., On a conjecture of Graham, J. Number Theory 27 (1987), 33–40. Google Scholar

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