Vela Mathematics Program: problems

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613 problems · 1/13Number SourcesGraph 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 decidable · $500erdos:19

Erdős problem 19

graph theorychromatic numberN/A

declared proved · $500erdos:21

Erdős problem 21

combinatoricsintersecting familyA3915992 sources

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 provederdos:57

Erdős problem 57

graph theorychromatic numbercyclesN/A

declared provederdos:58

Erdős problem 58

graph theorychromatic numbercyclesN/A

declared disprovederdos:59

Erdős problem 59

graph theoryturan numberN/A

declared openerdos:62

Erdős problem 62

graph theoryN/A

declared provederdos:63

Erdős problem 63

graph theorychromatic numbercyclesN/A

declared openerdos:65

Erdős problem 65

graph theorycyclesN/A

declared proved · $100erdos:72

Erdős problem 72

graph theorycyclesN/A

declared provederdos:73

Erdős problem 73

graph theoryN/A

declared provederdos:76

Erdős problem 76

graph theoryramsey theoryA060407

declared open · $250erdos:77

Erdős problem 77

graph theoryramsey theoryA059442

declared open · $100erdos:78

Erdős problem 78

graph theoryramsey theoryA0594422 sources

declared provederdos:79

Erdős problem 79

graph theoryramsey theoryN/A

declared openerdos:80

Erdős problem 80

graph theoryramsey theoryN/A

declared openerdos:81

Erdős problem 81

graph theorypossible2 sources

declared proved · $500erdos:83

Erdős problem 83

combinatoricsA071799 · A387635

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 proved · $100erdos:88

Erdős problem 88

graph theoryramsey theoryN/A

declared proved · $500erdos:95

Erdős problem 95

geometryconvexdistancespossible

declared openerdos:102

Erdős problem 102

geometryN/A

declared openerdos:103

Erdős problem 103

geometrydistancespossible

declared open · $100erdos:104

Erdős problem 104

geometryA003829

declared falsifiableerdos:106

f(n)

is the maximum total side length of

n

interior-disjoint squares packed in the unit square, is

f(k^2 + 1) = k

? An exact rational configuration packs

17

squares with total side length greater than

4

, refuting the identity at

k = 4

geometryN/A3 sources

declared disprovederdos:110

Erdős problem 110

graph theorychromatic numbercyclesN/A

declared openerdos:111

Erdős problem 111

graph theorychromatic numberset theoryN/A

declared openerdos:112

Erdős problem 112

graph theoryramsey theorypossible

declared disproved · $500erdos:113

Erdős problem 113

graph theoryturan numberN/A

declared falsifiable · $250erdos:114

Erdős problem 114

polynomialsanalysisN/A

declared provederdos:116

Erdős problem 116

polynomialsanalysisN/A

declared openerdos:117

Erdős problem 117

group theorypossible

declared disprovederdos:118

Erdős problem 118

set 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 provederdos:127

Erdős problem 127

graph theorypossible

declared openerdos:129

Erdős problem 129

graph theoryramsey theorypossible

declared openerdos:131

Let

F(N)

be the maximal size of

A\subseteq\{1,\ldots,N\}

such that no

a\in A

divides the sum of any nonempty subset of

A\setminus\{a\}

. Estimate

F(N)

. The lower bound

F(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)\leq N^{1/4+o(1)}

. The claimed new result is the matching upper bound

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)=N^{1/5+o(1)}

number theoryA0680632 sources

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