Problems
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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.
An n-divisor set contains a multiple of every integer from 1 to n. Umans and Wang proposed, as the arithmetic-progression form of their Strong (α,β)-Divisor Conjecture, that such a progression exists with few terms of bounded magnitude,…
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…
Let n_k be the least n > 2k such that (n-k)(n-k+1)…(n-1) has no prime factor in (k, 2k). Erdos conjectured a superpolynomial lower bound; for all large k, n_k > e^log^2 k / (20 loglog k).
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?
Let k≥ 3 and f_k(N) be the maximum of ∑_n∈ A1/n over all A⊆1,…,N containing no k subsets with the same pairwise least common multiple. Estimate f_k(N). The claimed answer: f_k(N)=(log N)^γ_k+o(1), where γ_k is a weighted generalization of…
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.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes. This is the ω = 2 integer case of a problem of Erdos and Graham, left as a conjecture by Butler, Erdos and Graham, who proved the ω = 3…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.