A sharpening of our old conjecture with Turán would state: If a_n < Cn^2 for all n then limsup f(n) = ∞. In fact, for what functions g(n) → ∞ does a_n < n^2 g(n) imply limsup f(n) = ∞? (500 dollars)

Erdős Problem #40 — Growth conditions $a_n<Cn^2$ forcing unbounded $f(n)$

Erdős

A sharpening of our old conjecture with Turán would state: If $a_n < Cn^2$ for all $n$ then $\limsup f(n) = \infty$ . In fact, for what functions $g(n) \to \infty$ does $a_n < n^2 g(n)$ imply $\limsup f(n) = \infty$ ? (500 dollars)

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Primary source

P. Erdős, Some of my favourite problems in number theory, combinatorics, and geometry, Resenhas IME-USP 2 (1995), 165-186.

3 weeks ago

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