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Erdős problem 698

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Is there some h(n)→∞h(n)\to \infty such that for all 2≤i<j≤n/22\leq i<j\leq n/2 gcd((ni),(nj))≥h(n)?\textrm{gcd}\left( \binom{n}{i},\binom{n}{j}\right) \geq h(n)?

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Problem row
sha256:711214b3aeb7796c94e6807eebde705cecd45a5e1bacd2a54dae1800799b5f66
Metadata
sha256:34b62416affccf224a17f2751b7cd3ec00b86951fceaae4a93188e35bda50824
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:0c8f6fcc6563fb4a17542c807edd481d08289b08c759ca7d484e683e7b698d34
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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