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

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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
@article{10_4153_CMB_1967_015_8,
     author = {Abbott, H. L. and Gardner, B.},
     title = {An {Extremal} {Problem} in {Number} {Theory}},
     journal = {Canadian mathematical bulletin},
     pages = {173--177},
     year = {1967},
     volume = {10},
     number = {2},
     doi = {10.4153/CMB-1967-015-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-015-8/}
}
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