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Problems · Vela Mathematics Program

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216 problems · 1/5NumberSourcesGraph view
declared disproved · $1000erdos:2
Erdős problem 2
number theorycovering systemsA160559
declared openerdos:5
Erdős problem 5
number theoryprimesA001223
declared disprovederdos:8
Erdős problem 8
number theorycovering systemsN/A
declared disproved · $100erdos:27
Erdős problem 27
number theorycovering systemsN/A
declared proved · $100erdos:29
Erdős problem 29
number theoryadditive basisN/A
declared provederdos:35
Erdős problem 35
number theoryadditive basisN/A
declared disprovederdos:37
Erdős problem 37
number theoryadditive combinatoricsN/A
declared provederdos:49
Erdős problem 49
number theoryprimesA365339 · A365474
declared provederdos:53
Erdős problem 53
number theoryadditive combinatoricspossible
declared solved · $100erdos:54
Erdős problem 54
number theoryramsey theoryN/A
declared solved · $250erdos:55
Erdős problem 55
number theoryramsey theoryN/A
declared disprovederdos:121
Erdős problem 121
number theorysquaresA028391 · A013928 · A372306 · A373319 · A372306 · A373178 · A360659 · A373114 · A143301
declared openerdos:122
Erdős problem 122
number theoryN/A
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 proved · $250erdos:144
Erdős problem 144
number theorydivisorsA005279
declared openerdos:148
Erdős problem 148
number theoryunit fractionsA076393 · A006585
declared provederdos:175
Erdős problem 175
number theorybinomial coefficientsN/A
declared proved · $500erdos:220
Erdős problem 220
number theoryA322144
declared openerdos:222
Erdős problem 222
number theorysquaresA001481 · A256435
declared provederdos:235
Erdős problem 235
number theoryN/A
declared proved (Lean)erdos:237
Erdős problem 237
number theoryprimesN/A4 sources
declared provederdos:240
Erdős problem 240
number theoryprimesN/A
declared openerdos:261
Erdős problem 261
number theoryN/A
declared openerdos:278
Erdős problem 278
number theorycovering systemsN/A
declared provederdos:284
Erdős problem 284
number theoryunit fractionspossible
declared provederdos:286
Erdős problem 286
number theoryunit fractionsN/A
declared provederdos:292
Erdős problem 292
number theoryunit fractionsA092671
declared openerdos:293
Erdős problem 293
number theoryunit fractionspossible
declared provederdos:294
Erdős problem 294
number theoryunit fractionspossible
declared solvederdos:297
Erdős problem 297
number theoryunit fractionsA092670
declared solvederdos:300
Erdős problem 300
number theoryunit fractionsA390393
declared openerdos:301
Erdős problem 301
number theoryunit fractionsA390394
declared provederdos:305
Erdős problem 305
number theoryunit fractionspossible
declared provederdos:308
Erdős problem 308
number theoryunit fractionspossible
declared disprovederdos:309
Erdős problem 309
number theoryunit fractionsA217693
declared provederdos:310
Erdős problem 310
number theoryunit fractionsN/A
declared openerdos:311
Erdős problem 311
number theoryunit fractionsN/A
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 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
declared openerdos:338
Erdős problem 338
number theoryadditive basisN/A
declared provederdos:339
Erdős problem 339
number theoryadditive basisN/A
declared provederdos:343
Erdős problem 343
number theorycomplete sequencesN/A
declared provederdos:344
Erdős problem 344
number theorycomplete sequencesN/A
declared openerdos:345
Erdős problem 345
number theorycomplete sequencesA0016612 sources
declared provederdos:356
Erdős problem 356
number theorypossible
declared solvederdos:360
Erdős problem 360
number theorypossible

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