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Combinatorics
Erdős problem 535
Let r≥3, and let fr(N) denote the size of the largest subset of {1,…,N}
such that no subset of size
r
has the same pairwise greatest common divisor between all
elements. Erdős [Er64] proved that
f3(N)>Nc/loglogN
for some constant
c>0
, and
conjectured this should also be an upper bound; here we state the conjectural upper bound
for all
r≥3
.
See also [536].
$2,685 bounty·1 piece from 1 person·last one 17 days ago
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A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
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