Geodesic
An Extremal Problem in Number Theory
Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 173-177

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

Let n and k be integers with n ≥ k ≥ 3. Denote by f(n, k) the largest positive integer for which there exists a set S of f (n, k) integers satisfying (i) and (ii) no k members of S have pairwise the same greatest common divisor. The problem of determining f(n, k) appears to be difficult. Erdős [2[ proved that there is an absolute constant c > 1 such that for every ∈ > 0 and every fixed k 1 provided n > no (k, ∈). In [l[ it i s proved that for every ∈ > 0 and every fixed k 
Abbott, H. L.; Gardner, B. An Extremal Problem in Number Theory. Canadian mathematical bulletin, Tome 10 (1967) no. 2, pp. 173-177. doi: 10.4153/CMB-1967-015-8
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[1] 1. Abbott, H. L., Some remarks on a combinatorial theorem of Erdős and Rado. Can. Math. Bull. vol. 9, no. 2 (1966) pages 155-160. Google Scholar

[2] 2. Erdős, P., On à problem in elementary number theory and a combinatorial problem. Math, of Comp.. vol. 18, no. 8. (1966), pages 644-646. Google Scholar

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