Skip to content

Erdős Problems

1,217 source-owned questions · 604 with a formal statement · searchable by statement, number, topic and source status.

Add a contributionCollection details
Collection coverage

Collection coverage

Source status, exact formal material, and reviewed Results are separate signals.

  • Open per source608
  • Resolved per source556
  • Other source status53
Exact formal statement available604 / 1,217
With Repository-reviewed evidence2 / 1,217
More filters

Coverage is source-observation coverage, not Problem completeness. Inspect coverage

Problems

1,217 Problems · 2 with reviewed evidence

14/26

NumberQuestionOpen
#625No statement retained — open to read what the source holdsopenNo formal declaration
#626No statement retained — open to read what the source holdsopenNo formal declaration
#627No statement retained — open to read what the source holdsopenNo formal declaration
#628Let GG be a graph with chromatic number kk containing no KkK_k. If a,b≥2a,b\geq 2 and a+b=k+1a+b=k+1 then must there exist two disjoint subgraphs of GG with chromatic numbers ≥a\geq a and ≥b\geq b respectively?falsifiableFormalized
#629No statement retained — open to read what the source holdsopenNo formal declaration
#630No statement retained — open to read what the source holdsprovedNo formal declaration
#631No statement retained — open to read what the source holdsprovedNo formal declaration
#632No statement retained — open to read what the source holdsdisprovedNo formal declaration
#633Which triangles can only be decomposed into a square number of congruent triangles?solvedFormalized
#634No statement retained — open to read what the source holdsopenNo formal declaration
#635No statement retained — open to read what the source holdsopenNo formal declaration
#636No statement retained — open to read what the source holdsprovedNo formal declaration
#637No statement retained — open to read what the source holdsprovedNo formal declaration
#638No statement retained — open to read what the source holdsopenNo formal declaration
#639Is it true that if the edges of KnK_n are 2-coloured then there are at most n2/4n^2/4 many edges which do not occur in a monochromatic triangle?proved (Lean)Formalized
#640No statement retained — open to read what the source holdsopenNo formal declaration
#641No statement retained — open to read what the source holdsdisprovedNo formal declaration
#642No statement retained — open to read what the source holdsopenNo formal declaration
#643No statement retained — open to read what the source holdsopenNo formal declaration
#644No statement retained — open to read what the source holdsopenNo formal declaration
#645If ℕ is 22-coloured then there must exist a monochromatic three-term arithmetic progression x,x+d,x+2dx,x+d,x+2d such that d>xd>x.proved (Lean)Formalized
#646Let p1,…,pkp_1,\ldots,p_k be distinct primes. Are there infinitely many nn such that n!n! is divisible by an even power of each of the pip_i?proved (Lean)Formalized
#647Let τ(n)\tau(n) count the number of divisors of nn. Is there some n>24n > 24 such that max⁡m<n(m+τ(m))≤n+2? \max_{m < n}(m + \tau(m)) \leq n + 2? verifiableFormalized
#648Let g(n)g(n) denote the largest tt such that there exist integers 2≤a1<a2<⋯<at<n2\leq a_1<a_2<\cdots <a_t <n such that P(a1)>P(a2)>⋯>P(at)P(a_1)>P(a_2)>\cdots >P(a_t) where P(m)P(m) is the greatest prime factor of mm. Estimate g(n)g(n).solved (Lean)Formalized
#649Let P(m)P(m) denote the greatest prime factor of mm. Is it true that, for any two primes p,qp,q, there exists some integer nn such that P(n)=pP(n)=p and P(n+1)=qP(n+1)=q?disproved (Lean)Formalized
#650Let f(m)f(m) be such that if A⊆{1,…,N}A\subseteq \{1,\ldots,N\} has ∣A∣=m\lvert A\rvert=m then every interval in [1,∞)[1,\infty) of length 2N2N contains ≥f(m)\geq f(m) many distinct integers b1,…,brb_1,\ldots,b_r where each bib_i is divisible by some ai∈Aa_i\in A, where a1,…,ara_1,\ldots,a_r are distinct.solved (Lean)Formalized
#651No statement retained — open to read what the source holdsdisprovedNo formal declaration
#652No statement retained — open to read what the source holdsprovedNo formal declaration
#653Let x1,…,xn∈R2x_1,\ldots,x_n\in \mathbb{R}^2 and let R(xi)=#{∣xj−xi∣:j≠i}R(x_i)=\#\{ \lvert x_j-x_i\rvert : j\neq i\}, where the points are ordered such that R(x1)≤⋯≤R(xn).R(x_1)\leq \cdots \leq R(x_n). Let g(n)g(n) be the maximum number of distinct values the R(xi)R(x_i) can take. Is it true that g(n)≥(1−o(1))ng(n) \geq (1-o(1))n?openFormalized
#654No statement retained — open to read what the source holdsopenNo formal declaration
#655Let x1,…,xn∈R2x_1,\ldots,x_n\in \mathbb{R}^2 be such that no circle whose centre is one of the xix_i contains three other points. Are there at least (1+c)n2(1+c)\frac{n}{2} distinct distances determined between the xix_i, for some constant c>0c>0 and all nn sufficiently large?openFormalized
#656No statement retained — open to read what the source holdsprovedNo formal declaration
#657No statement retained — open to read what the source holdsopenNo formal declaration
#658No statement retained — open to read what the source holdsproved (Lean)No formal declaration
#659Is there a set of nn points in R2\mathbb{R}^2 such that every subset of 44 points determines at least 33 distances, yet the total number of distinct distances is ≪nlog⁡n\ll \frac{n}{\sqrt{\log n}}?proved (Lean)Formalized
#660No statement retained — open to read what the source holdsopenNo formal declaration
#661No statement retained — open to read what the source holdsopenNo formal declaration
#662No statement retained — open to read what the source holdsopenNo formal declaration
#663No statement retained — open to read what the source holdsopenNo formal declaration
#664No statement retained — open to read what the source holdsdisprovedNo formal declaration
#665No statement retained — open to read what the source holdsopenNo formal declaration
#666Let QnQ_n be the nn-dimensional hypercube graph (so that QnQ_n has 2n2^n vertices and n2n−1n2^{n-1} edges). Is it true that, for every ϵ>0\epsilon>0, if nn is sufficiently large, every subgraph of QnQ_n with ≥ϵn2n−1\geq \epsilon n2^{n-1} many edges contains a C6C_6?disproved (Lean)Formalized
#667No statement retained — open to read what the source holdsopenNo formal declaration
#668No statement retained — open to read what the source holdsopenNo formal declaration
#669No statement retained — open to read what the source holdsopenNo formal declaration
#670No statement retained — open to read what the source holdsopenNo formal declaration
#671No statement retained — open to read what the source holdsopenNo formal declaration
#672Can the product of an arithmetic progression of positive integers n,n+d,...,n+(k−1)dn, n + d, ..., n + (k - 1)d of length ≥ 4, with (n,d)=1(n, d) = 1, be a perfect power?verifiableFormalized

Search problems.science

Find a Problem, Result, source, or page