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declared solved · formalized · $100erdos:119
For unit-modulus complex numbers ziz_i, let pn(z)=∏i≤n(z−zi)p_n(z)=\prod_{i\le n}(z-z_i) and Mn=max⁡∣z∣=1∣pn(z)∣M_n=\max_{|z|=1}|p_n(z)|. Erdős's prize question: is there c>0c>0 with ∑k≤nMk>n1+c\sum_{k\le n} M_k > n^{1+c}?
analysispolynomialsN/A4 sources
declared solvederdos:320
Let S(N)S(N) count the distinct values of ∑n∈A1/n\sum_{n\in A} 1/n over A⊆{1,…,N}A\subseteq\{1,\dots,N\}. Estimate S(N)S(N).
number theoryunit fractionsA0722072 sources
declared solved · formalizederdos:321
What is the largest A⊆{1,…,N}A\subseteq\{1,\dots,N\} such that all subset sums ∑n∈S1/n\sum_{n\in S}1/n (over S⊆AS\subseteq A) are distinct?
number theoryunit fractionsA384927 · A3915923 sources
declared solvederdos:603
Erdős problem 603
combinatoricsset theoryN/A3 sources
declared solvederdos:690
Erdős problem 690
number theorypossible4 sources
declared solvederdos:858
Erdős problem 858
number theoryprimitive setsN/A4 sources
declared solved · formalizederdos:888
(fun n => ↑(Nat.findGreatest (Erdos888.p n) n)) =Θ[Filter.atTop] fun n => ↑n * Real.log (Real.log ↑n) / Real.log ↑n
number theorysquaresA3875845 sources
declared solvederdos:896
Erdős problem 896
number theorypossible3 sources
declared solvederdos:948
Erdős problem 948
number theoryramsey theoryN/A3 sources
declared solvederdos:1089
Erdős problem 1089
geometrydistancespossible3 sources
declared solvederdos:1091
Erdős problem 1091
geometrychromatic numberN/A3 sources
declared solvederdos:1195
Erdős problem 1195
number theorypossible3 sources
declared solvederdos:1202
Erdős problem 1202
number theoryprimespossible3 sources

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