Vela Mathematics Program: problems

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613 problems · 9/13Number SourcesGraph view

declared provederdos:823

Erdős problem 823

number theoryN/A

declared openerdos:824

Erdős problem 824

number theorypossible

declared openerdos:827

Erdős problem 827

geometrypossible

declared openerdos:831

Erdős problem 831

geometrypossible

declared disprovederdos:832

Erdős problem 832

graph theoryhypergraphschromatic numberpossible

declared provederdos:833

Erdős problem 833

graph theoryhypergraphschromatic numberpossible

declared solvederdos:834

Erdős problem 834

graph theoryhypergraphsN/A

declared openerdos:836

Erdős problem 836

graph theoryhypergraphschromatic numberN/A2 sources

declared openerdos:837

Erdős problem 837

graph theoryhypergraphsN/A

declared openerdos:838

Erdős problem 838

geometryconvexpossible

declared openerdos:839

Erdős problem 839

number theoryN/A

declared openerdos:840

Erdős problem 840

additive combinatoricssidon setsN/A

declared solvederdos:841

Erdős problem 841

number theoryA092487

declared provederdos:842

Erdős problem 842

graph theorychromatic numberN/A

declared provederdos:843

Erdős problem 843

number theoryN/A

declared openerdos:852

Erdős problem 852

number theoryprimesA001223 · A053597 · A0785152 sources

declared openerdos:854

Erdős problem 854

number theoryA389839 · A048670

declared openerdos:856

Let

k\geq 3

and

f_k(N)

be the maximum of

\sum_{n\in A}\frac{1}{n}

over all

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

containing no

k

subsets with the same pairwise least common multiple. Estimate

f_k(N)

. The claimed answer:

f_k(N)=(\log N)^{\gamma_k+o(1)}

, where

\gamma_k

is a weighted generalization of the Tang-Zhang sunflower capacity.

number theorypossible3 sources

declared solvederdos:858

Erdős problem 858

number theoryprimitive setsN/A4 sources

declared openerdos:860

Erdős problem 860

number theoryprimesA048670 · A058989

declared solvederdos:861

Erdős problem 861

number theorysidon setsA143824 · A227590 · A003022 · A143823

declared provederdos:863

Erdős problem 863

number theorysidon setsadditive combinatoricsN/A3 sources

declared openerdos:864

Erdős problem 864

number theorysidon setsadditive combinatoricsA3891822 sources

declared openerdos:866

Estimate the least excess

g_k(N)

forcing

k

integers whose pairwise sums all lie in a dense subset of

\{1, \dots, 2N\}

; in particular, determine the positive variant

h_4(n)

number theoryadditive combinatoricspossible5 sources

declared disprovederdos:869

Erdős problem 869

number theoryadditive basisN/A

declared openerdos:870

Let

k\geq 3

and

A

be an additive basis of order

k

. Does there exist a constant

c=c(k)>0

such that if

r(n)\geq c\log n

for all large

n

(where

r(n)

counts representations of

n

as a sum of at most

k

elements of

A

) then

A

must contain a minimal basis of order

k

? The claimed answer is no, for every

k\geq 3

number theoryadditive basisN/A3 sources

declared provederdos:874

Erdős problem 874

number theoryadditive combinatoricspossible

declared openerdos:875

Erdős problem 875

additive combinatoricsN/A2 sources

declared openerdos:876

Erdős problem 876

additive combinatoricsN/A

declared provederdos:877

Erdős problem 877

additive combinatoricsA121269 · possible

declared openerdos:878

Erdős problem 878

number theoryA339378 · possible

declared openerdos:879

Erdős problem 879

number theoryA186736

declared provederdos:880

Erdős problem 880

number theoryadditive basisN/A

declared solvederdos:882

Erdős problem 882

number theoryprimitive setspossible

declared openerdos:883

Erdős problem 883

number theorygraph theoryN/A

declared openerdos:892

Erdős problem 892

number theoryprimitive setsN/A

declared provederdos:894

Erdős problem 894

number theoryramsey theoryN/A

declared provederdos:895

Erdős problem 895

additive combinatoricsgraph theoryN/A

declared solvederdos:896

Erdős problem 896

number theorypossible3 sources

declared provederdos:900

Erdős problem 900

graph theoryN/A

declared openerdos:901

Erdős problem 901

combinatoricshypergraphspossible

declared openerdos:902

Erdős problem 902

graph theoryA362137

declared provederdos:903

Erdős problem 903

combinatoricsN/A

declared provederdos:908

Erdős problem 908

analysisN/A

declared provederdos:909

Erdős problem 909

analysistopologyN/A

declared disprovederdos:910

Erdős problem 910

topologyN/A

declared openerdos:911

Erdős problem 911

graph theoryramsey theoryN/A

declared solvederdos:915

Erdős problem 915

graph theoryN/A

declared provederdos:916

Erdős problem 916

graph theorycyclesN/A

declared openerdos:917

Erdős problem 917

graph theorychromatic numberN/A

Problems · Vela Mathematics Program

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