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
Can there be a finite covering system of the integers with distinct moduli, all of which are odd and greater than 1?
Let A ⊂ N be infinite with no distinct a, b, c ∈ A such that a | (b + c) with b, c > a. Can |A ∩ [1, N]|/√N have positive lower limit? Must every such A fall below N^1-c infinitely often?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Does there exist A=a_1<a_2<…⊂ N which is a minimal basis of order 2 (every large integer is the sum of 2 elements from A, and no proper subset of A has this property) such that lim_k→ ∞a_k/k^2=c for some c≠ 0? A claimed construction gives…
If A(x) counts integers satisfying the Sylow divisor condition, determine the constant c in A(x)/x = exp(-(c + o(1)) √log x loglog x). The claimed exact value is c = 1/(2√log 2).
For |A| = n, how small can the cofactor set Q(A) = a / gcd(a,b) : a, b ∈ A be? The answer is h(n) = n^1/2 + o(1): a new upper bound h(n) ≤ n^1/2 exp(O(√log n)) matches the classical lower bound.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Bounds the weighted sum ∑ 1/(a log a) taken over primitive sets of integers (sets where no element divides another).
What is the largest A⊆1,…,N such that all subset sums ∑_n∈ S1/n (over S⊆ A) are distinct?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For every finite set A⊂ Z with |A|≥ 2, define C(A)=log(|A+A|/|A|)/log(|A-A|/|A|). Determine the largest possible value of C(A), equivalently the least universal exponent c such that |A+A|/|A| ≤ (|A-A|/|A|)^c for every such set A. The…
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.
Let A=1≤ a_1< a_2<… be a set of integers such that Abackslash B is complete for any finite subset B and not complete for any infinite subset B. If a_n+1/a_n ≥ 1+ε for all n, must lim_n a_n+1/a_n=(1+√5)/2? Under the reading where the ratio…
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.
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.