Is it true that $f(n,k) 0$ and for all $n > 0$?

Erdős problem 20 · problems.science

Is it true that $f(n,k) < c_k^n$ for some constant $c_k>0$ and for all $n > 0$ ?

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Problem row: sha256:68a367ae8024a6fd122a86d3f8b78743e375c867000d655ffddef7619a5debb8
Metadata: sha256:37c7af53740196b6e993ed6bf92018cccb677d7557fa4f2f2c42f71534f66e63
Observation: sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
Content: sha256:ec5ba5fcbee6e751d9952805e4ab34b74fafb6a4dda1451d8f1280d07c3d800f

Repository: sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection: sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
Source commit: 2415f78e850aeee50afdca525c6f2e0ea606f207