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VibeMathed records no statement for this problem. See erdosproblems.com for the original.

Does the conjectured universal formula for normalized alternating syzygy power sums of numerical semigroup rings hold for every index?

For odd k with gcd(n,k) = gcd(n+1,k) = 1, is N_k(n) ≡ ⌊ (k+1)/4 ⌋ pmod 2, where N_k(n) counts pairs 1 ≤ b_i ≤ (k-1)/2 with b_1 + b_2 ≥ (k+1)/2 and b_2 ≡ n b_1 pmod k? Conjectured by Chen and Gendron; its proof removes a conditional step in…

If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four - that is, is every cograph power graph chordal?

Does the sum of the reciprocals of all primitive pseudoperfect numbers converge?

Let a,b,c>1 be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form a^k b^l c^m (k,l,m≥ 0), none dividing another?

Is the number of nonnesting permutations of 1,1,…,n,n avoiding both 1132 and 3312 equal to 3^n - 3 · 2^n-1 + 1 for every n ≥ 1?

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 X = (X_1,…,X_n) be a centered Gaussian vector, not necessarily nondegenerate. Then, for every α_1,…,α_n > 0, E[∏_i=1^n |X_i|^α_i] ≥ ∏_i=1^n E[|X_i|^α_i]. Moreover, if Var(X_i) > 0 for every i, then equality holds if and only if…

The multivariate independence polynomial is the partition function of the hard-core model with per-vertex fugacities. The paper proves a lower bound extending to the multivariate setting a result Tao proved in the univariate case, and…

For positive integers d and k, let n_k(d) be the maximum order of a graph of maximum degree at most d and diameter at most k. It is shown that lim_d → ∞n_k(d)/d^k = 1 for every fixed k, thereby resolving the asymptotic degree-diameter…

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

With N = 2^k - 1 and wt(n) the binary Hamming weight, Tu and Deng conjectured that for every 1 ≤ t ≤ N-1 at most 2^k-1 pairs (a,b) satisfy a + b ≡ t pmod N and wt(a) + wt(b) < k. Proved in full.

For f(z) = ∏_i=1^n (z - z_i) with all |z_i| ≤ 1, let ρ(f) be the radius of the largest disc contained in z : |f(z)| < 1. Is ρ(f) ≫ 1/n? The worst case is now known to be Θ(1/n), with the explicit bound ρ(f) ≥ (log 2)/n.

Give an explicit profinite presentation of Gal(overlineQ_2 / Q_2). The tame local cases were settled by the early 1980s; the dyadic case was the last one missing. The new presentation has four generators, two word relations and a pro-2…

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.

Whether there are infinitely many integers a, b, n with a, b ≥ ε n such that a!· b! divides n!·(a+b-n)! while a+b exceeds n by more than C·log n.

Let X_1,…,X_n be independent nonnegative random variables with EX_i ≤ 1, and let S be their sum. Is P(S < ES + 1) ≥ 1/e? Feige proved the constant 1/13 and conjectured the sharp 1/e. Three independent July 2026 proofs settle it, both…