Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
4 problems
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…
Must every graph with n vertices and δ n^2 edges contain large subgraphs in which every two edges lie on specified short cycles? A dense high-girth construction refutes the statement when δ may shrink with n.
Let A⊂N be infinite. Must there exist some k≥ 1 such that almost all integers have a divisor of the form a+k for some a∈ A? The question as posed follows negatively from Davenport–Erdős (1951). The AI result settles Tenenbaum's harder…
If n planar points have no four concyclic, must some point determine (1 - o(1))n distinct distances? Failing that, can one always force more than (1/3 + c)n?