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declared disprovederdos:37
Erdős problem 37
number theoryadditive combinatoricsN/A
declared provederdos:53
Erdős problem 53
number theoryadditive combinatoricspossible
declared proved · $500erdos:140
Erdős problem 140
additive combinatoricsarithmetic progressionsA003002
declared openerdos:169
Erdős problem 169
additive combinatoricsarithmetic progressionsA005346
declared provederdos:171
Erdős problem 171
additive combinatoricscombinatoricsA156989
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 provederdos:179
Erdős problem 179
additive combinatoricsarithmetic progressionspossible
declared provederdos:185
Erdős problem 185
additive combinatoricsA003142
declared solvederdos:186
Erdős problem 186
additive combinatoricsA389784
declared openerdos:187
Erdős problem 187
additive combinatoricsramsey theoryN/A
declared solvederdos:190
Erdős problem 190
additive combinatoricsarithmetic progressionspossible
declared openerdos:201
Erdős problem 201
additive combinatoricsarithmetic progressionsA003002 · A003003 · A003004 · A003005 · possible
declared openerdos:271
Erdős problem 271
additive combinatoricsarithmetic progressionsA005487
declared openerdos:335
Erdős problem 335
number theoryadditive combinatoricsN/A2 sources
declared decidableerdos:475
Erdős problem 475
number theoryadditive combinatoricsN/A
declared openerdos:483
Erdős problem 483
number theoryadditive combinatoricsramsey theoryA030126
declared provederdos:656
Erdős problem 656
number theoryadditive combinatoricsN/A
declared proved (Lean)erdos:658
Erdős problem 658
additive combinatoricspossible4 sources
declared solvederdos:721
Erdős problem 721
number theoryadditive combinatoricsramsey theoryA171081
declared disprovederdos:763
Erdős problem 763
number theoryadditive combinatoricsN/A
declared disprovederdos:764
Erdős problem 764
number theoryadditive combinatoricsN/A
declared provederdos:772
Erdős problem 772
number theorysidon setsadditive combinatoricspossible
declared disprovederdos:781
Erdős problem 781
additive combinatoricspossible
declared openerdos:787
Erdős problem 787
additive combinatoricspossible
declared openerdos:788
Erdős problem 788
additive combinatoricspossible3 sources
declared openerdos:790
Erdős problem 790
additive combinatoricspossible
declared openerdos:791
Erdős problem 791
additive combinatoricsA066063
declared openerdos:792
Erdős problem 792
additive combinatoricspossible2 sources
declared provederdos:806
Erdős problem 806
additive combinatoricspossible
declared disprovederdos:808
Erdős problem 808
additive combinatoricsgraph theoryN/A
declared openerdos:819
Erdős problem 819
additive combinatoricspossible2 sources
declared openerdos:840
Erdős problem 840
additive combinatoricssidon setsN/A
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 gk(N)g_k(N) forcing kk integers whose pairwise sums all lie in a dense subset of {1,…,2N}\{1, \dots, 2N\}; in particular, determine the positive variant h4(n)h_4(n).
number theoryadditive combinatoricspossible5 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 provederdos:895
Erdős problem 895
additive combinatoricsgraph theoryN/A
declared provederdos:984
Erdős problem 984
arithmetic progressionsadditive combinatoricsN/A
declared open (Lean)erdos:1112
Erdős problem 1112
additive combinatoricsN/A
declared provederdos:1179
Erdős problem 1179
additive combinatoricsprobabilityN/A
declared solvederdos:1185
Erdős problem 1185
additive combinatoricsarithmetic progressionsN/A
declared openerdos:1186
What is the minimum asymptotic density δk\delta_k of monochromatic kk-term arithmetic progressions in every two-colouring of {1,…,n}\{1, \dots, n\}? The exact certificate gives δ3=117/2192\delta_3 = 117/2192, matching the known 548-bead colouring.
additive combinatoricsarithmetic progressionspossible2 sources
declared solvederdos:1187
Erdős problem 1187
number theoryprimesadditive combinatoricsN/A3 sources
declared open · $1000erdos:1191
Erdős problem 1191
additive combinatoricssidon setspossible
declared openerdos:1194
Erdős problem 1194
additive combinatoricsadditive basissidon setspossible2 sources
declared disprovederdos:1198
Erdős problem 1198
additive combinatoricsramsey theoryN/A
declared provederdos:1213
Erdős problem 1213
additive combinatoricspossible

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