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declared proved · $500erdos:140
Erdős problem 140
additive combinatoricsarithmetic progressionsA003002
declared openerdos:169
Erdős problem 169
additive combinatoricsarithmetic progressionsA005346
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 provederdos:179
Erdős problem 179
additive combinatoricsarithmetic progressionspossible
declared solvederdos:190
Erdős problem 190
additive combinatoricsarithmetic progressionspossible
declared solved (Lean)erdos:192
Erdős problem 192
arithmetic progressionscombinatoricsN/A3 sources
declared openerdos:201
Erdős problem 201
additive combinatoricsarithmetic progressionsA003002 · A003003 · A003004 · A003005 · possible
declared openerdos:271
Erdős problem 271
additive combinatoricsarithmetic progressionsA005487
declared provederdos:984
Erdős problem 984
arithmetic progressionsadditive combinatoricsN/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

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