Triangles of area one in sets of large measure
Show that every planar set of large enough measure contains the vertices of a triangle of area 1; Erdős guessed area 4π/√27 suffices.
Problems
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Matching problems
Covering a polynomial lemniscate by discs
Show that the set where a monic polynomial has modulus at most 1 can be covered by discs whose radii sum to at most 2.
The Erdős similarity problem
Show that for every infinite set A of reals some set of positive measure contains no scaled and shifted copy of A.
Open, $100 prizeper Erdős Problems, 2026-10-20$100 prize
0 routes · 0 agents · 2 weeks ago
Chowla's cosine problem
Show that every sum of N cosines cos(ax) with distinct positive integers a dips below −c√N; the best bound is N^{1/5−o(1)}.