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28 problemsGraph view
declared proved · $500erdos:95
Erdős problem 95
geometryconvexdistancespossible
declared openerdos:103
Erdős problem 103
geometrydistancespossible
declared open · $100erdos:132
Erdős problem 132
distancesN/A
declared disproved · $250erdos:135
Erdős problem 135
distancesgeometrypossible
declared openerdos:217
Erdős problem 217
geometrydistancespossible
declared solvederdos:223
Erdős problem 223
geometrydistancespossible
declared provederdos:232
Erdős problem 232
geometrydistancesN/A
declared open · $500erdos:604
Erdős problem 604
geometrydistancespossible
declared provederdos:605
Erdős problem 605
geometrydistancespossible
declared provederdos:652
Erdős problem 652
geometrydistancesN/A2 sources
declared openerdos:654
If nn planar points have no four concyclic, must some point determine (1−o(1))n(1 - o(1))n distinct distances? Failing that, can one always force more than (1/3+c)n(1/3 + c)n?
geometrydistancespossible3 sources
declared openerdos:657
Erdős problem 657
geometrydistancespossible
declared openerdos:660
Erdős problem 660
geometrydistancesconvexpossible
declared open · $50erdos:661
Erdős problem 661
geometrydistancespossible
declared openerdos:662
Among sufficiently large one-separated planar point sets, does the triangular lattice maximize the number of distances below each threshold? Explicit rational oblique lattices beat the triangular lattice under several closed- and strict-shell readings.
geometrydistancesN/A3 sources
declared openerdos:668
Erdős problem 668
geometrydistancesA385657
declared openerdos:670
Erdős asked whether every nn-point set in Euclidean space whose pairwise distances are mutually at least 1 apart must have diameter at least (1+o(1))n2(1+o(1))n^2. Disproved: an explicit high-dimensional construction beats the conjectured constant.
geometrydistancesN/A2 sources
declared provederdos:754
Erdős problem 754
geometrydistancespossible
declared openerdos:953
What is the largest possible measure of a subset of a radius-RR disk in R2\mathbb{R}^2 containing no pair of points at a positive integer distance? A Poisson-Bessel kernel argument gives M(R)≪R1/2M(R) \ll R^{1/2}; with Sárközy's lower construction, M(R)=R1/2+o(1)M(R) = R^{1/2 + o(1)}.
geometrydistancesN/A3 sources
declared openerdos:956
Erdős problem 956
geometrydistancesconvexpossible2 sources
declared provederdos:957
Erdős problem 957
geometrydistancesN/A
declared openerdos:1083
Erdős problem 1083
geometrydistancesA186704 · possible
declared openerdos:1086
Erdős problem 1086
geometrydistancespossible
declared openerdos:1087
Erdős problem 1087
geometrydistancespossible
declared solvederdos:1089
Erdős problem 1089
geometrydistancespossible3 sources
declared independenterdos:1127
Erdős problem 1127
geometrydistancesset theoryN/A
declared openerdos:1207
Erdős problem 1207
geometrydistancespossible
declared openerdos:1208
Erdős problem 1208
geometrydistancesA193838 · A271490 · possible2 sources

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