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Erdős problem 920

Is it true that, for k4k\geq 4, fk(n)n11k1(logn)ckf_k(n) \gg \frac{n^{1-\frac{1}{k-1}}}{(\log n)^{c_k}} for some constant ck>0c_k>0?

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Problem row
sha256:1aa053ca3ce54261582739f7a652b546f1f0216622e2c2554af8928958cb6fa9
Metadata
sha256:700da84e5cfa9ea9812512a60cba68ce0649a19686463053c827f272001562b8
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
Content
sha256:dbbf57f90790b754dbc95b4d309177f6aa53206dccd852f1a51be065a09e9ab2
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
Source commit
2415f78e850aeee50afdca525c6f2e0ea606f207

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