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285 problems · 1/6NumberSourcesGraph view
declared openerdos:5
Erdős problem 5
number theoryprimesA001223
declared openerdos:62
Erdős problem 62
graph theoryN/A
declared openerdos:65
Erdős problem 65
graph theorycyclesN/A
declared open · $250erdos:77
Erdős problem 77
graph theoryramsey theoryA059442
declared open · $100erdos:78
Erdős problem 78
graph theoryramsey theoryA0594422 sources
declared openerdos:80
Erdős problem 80
graph theoryramsey theoryN/A
declared openerdos:81
Erdős problem 81
graph theorypossible2 sources
declared openerdos:84
Erdős problem 84
graph theorycyclespossible
declared open · $100erdos:86
Erdős problem 86
graph theoryA245762
declared openerdos:87
Erdős problem 87
graph theoryramsey theoryA059442 · possible
declared openerdos:102
Erdős problem 102
geometryN/A
declared openerdos:103
Erdős problem 103
geometrydistancespossible
declared open · $100erdos:104
Erdős problem 104
geometryA003829
declared openerdos:111
Erdős problem 111
graph theorychromatic numberset theoryN/A
declared openerdos:112
Erdős problem 112
graph theoryramsey theorypossible
declared openerdos:117
Erdős problem 117
group theorypossible
declared openerdos:122
Erdős problem 122
number theoryN/A
declared openerdos:129
Erdős problem 129
graph theoryramsey theorypossible
declared openerdos:131
Let F(N)F(N) be the maximal size of A⊆{1,…,N}A\subseteq\{1,\ldots,N\} such that no a∈Aa\in A divides the sum of any nonempty subset of A∖{a}A\setminus\{a\}. Estimate F(N)F(N). The lower bound F(N)≫N1/5F(N)\gg N^{1/5} is classical, from constructions of Erdős and Csaba, and every non-dividing set is non-averaging, which gave F(N)≤N1/4+o(1)F(N)\leq N^{1/4+o(1)}. The claimed new result is the matching upper bound F(N)≤N1/5+o(1)F(N)\leq N^{1/5+o(1)}, obtained by running the Pham-Zakharov density-increment argument one dimension lower through a projective normalization, hence F(N)=N1/5+o(1)F(N)=N^{1/5+o(1)}.
number theoryA0680632 sources
declared open · $100erdos:132
Erdős problem 132
distancesN/A
declared openerdos:148
Erdős problem 148
number theoryunit fractionsA076393 · A006585
declared openerdos:149
Erdős problem 149
graph theoryN/A
declared openerdos:151
Erdős problem 151
graph theorypossible
declared openerdos:159
Erdős problem 159
graph theoryramsey theorypossible
declared open · $500erdos:161
Erdős problem 161
combinatoricsramsey theorydiscrepancyN/A2 sources
declared openerdos:162
Erdős problem 162
combinatoricsramsey theorydiscrepancyN/A
declared open · $250erdos:165
Erdős problem 165
graph theoryramsey theoryA0007912 sources
declared openerdos:169
Erdős problem 169
additive combinatoricsarithmetic progressionsA005346
declared openerdos:173
Erdős problem 173
geometryramsey theoryN/A
declared openerdos:174
Erdős problem 174
geometryramsey theoryN/A
declared openerdos:176
Let N(k,ℓ)N(k, \ell) be the least NN such that every f:[N]→{−1,1}f : [N] \to \{-1, 1\} has a kk-term arithmetic progression PP with ∣∑n∈Pf(n)∣≥ℓ|\sum_{n \in P} f(n)| \ge \ell. In particular, is N(k,2)≤CkN(k, 2) \le C^k?
additive combinatoricsarithmetic progressionsdiscrepancypossible3 sources
declared openerdos:177
Erdős problem 177
discrepancyarithmetic progressionsN/A
declared openerdos:181
Erdős problem 181
graph theoryramsey theorypossible
declared openerdos:187
Erdős problem 187
additive combinatoricsramsey theoryN/A
declared openerdos:201
Erdős problem 201
additive combinatoricsarithmetic progressionsA003002 · A003003 · A003004 · A003005 · possible
declared openerdos:217
Erdős problem 217
geometrydistancespossible
declared openerdos:222
Erdős problem 222
number theorysquaresA001481 · A256435
declared openerdos:256
Erdős problem 256
analysisN/A
declared openerdos:261
Erdős problem 261
number theoryN/A
declared openerdos:265
Erdős problem 265
irrationalityN/A
declared openerdos:271
Erdős problem 271
additive combinatoricsarithmetic progressionsA005487
declared openerdos:278
Erdős problem 278
number theorycovering systemsN/A
declared openerdos:293
Erdős problem 293
number theoryunit fractionspossible
declared openerdos:301
Erdős problem 301
number theoryunit fractionsA390394
declared openerdos:311
Erdős problem 311
number theoryunit fractionsN/A
declared openerdos:322
Erdős problem 322
number theorypowersA025456 · A025418
declared openerdos:327
Erdős problem 327
number theoryunit fractionsA3849272 sources
declared openerdos:334
Erdős problem 334
number theoryA062241 · A045535
declared openerdos:335
Erdős problem 335
number theoryadditive combinatoricsN/A2 sources
declared openerdos:336
If h(r)h(r) is the maximal finite exact order attainable by an additive basis of order at most rr, what is lim⁡r→∞h(r)/r2\lim_{r \to \infty} h(r)/r^2? The candidate proof identifies the sharp limit 1/31/3.
number theoryadditive basispossible2 sources

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