Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.
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For any natural number N, let C(N) denote the largest cardinality of a subset A of 1,…,N with the property that ab+1 is square-free for all a,b ∈ A. Establish upper and lower bounds for C(N) that are as strong as possible.
For a natural number N, let C(N) be the largest quantity such that N! can be factored into N factors that are greater than or equal to C(N) (see OEIS A034258). Establish upper and lower bounds on C(N) that are as strong as possible.
