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.
86 problems
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
How large must y(ε, n) be so that every interval (x, x+y) contains at most ε y integers having a divisor in (n, 2n)? The candidate proof gives the sharp fixed-ε order y = Θ_ε(n), uniformly in the translate.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
In the circle of Kummer's regular primes and Vandiver's conjecture, the paper proves that almost all primes are partially regular, yielding a partial Vandiver theorem for a density-one set of primes, with consequences for Kubota-Leopoldt…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Huang, Jiang and Oblomkov conjectured that the Eulerian q-series counting commuting pairs of nilpotent matrices with X^a = Y^b equals an explicit theta-and-eta product, making the point count essentially modular. The conjecture is layered…
If Sidon sets A, B ⊆ 1, …, N satisfy (A-A) ∩ (B-B) = 0, must binom|A|2 + binom|B|2 ≤ binomf(N)2 + O(1), where f(N) is the largest Sidon-set size in [N] - and can the bound be improved by a fixed proportion when |A| = |B|?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
If n_1 < n_2 < … with n_k+1/n_k ≥ c > 1, must ∑_k 1/F_n_k be irrational? The proposed proof closes the range 1 < c < 2 left open by earlier criteria.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Let S(N) count the distinct values of ∑_n∈ A 1/n over A⊆1,…,N. Estimate S(N).
Ballantine, Beck, Feigon and Maurischat introduced the subsum polynomial sp(λ,x) := ∏_i (1+x^λ_i) attached to an integer partition λ, studied rational functions built by summing reciprocals of these polynomials over natural classes of…
If A is a forbidden-divisor set with |A ∩ [1,x]| = o(√x) and B = b_1 < b_2 < … the sifted set, must x^-1 ∑_b_i < x (b_i+1 - b_i)^2 converge to a finite limit?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
If h(r) is the maximal finite exact order attainable by an additive basis of order at most r, what is lim_r → ∞ h(r)/r^2? The candidate proof identifies the sharp limit 1/3.
For the least k at which the small-prime part of binomnk exceeds n^2, how large can f(n) be?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.