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Erdős Problems

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

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  • Open per source608
  • Resolved per source556
  • Other source status53
Exact formal statement available604 / 1,217
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Problems

12 Problems · 1 with reviewed evidence

SelectNumberQuestionOpen
#93If nn distinct points in R2\mathbb{R}^2 form a convex polygon then they determine at least ⌊n2⌋\lfloor \frac{n}{2}\rfloor distinct distances.Source says proved (Lean)Formalized
#94Suppose nn points in R2\mathbb{R}^2 determine a convex polygon and the set of distances between them is {u1,…,ut}\{u_1,\ldots,u_t\}. Suppose uiu_i appears as the distance between f(ui)f(u_i) many pairs of points. Then ∑if(ui)2≪n3.\sum_i f(u_i)^2 \ll n^3.Source says proved (Lean)FormalizedResult here accepted
#95No statement retained — open to read what the source holdsSource says provedNo formal declaration
#96This lemma confirms that the set of possible unit-distance counts is bounded above, which ensures that taking the supremum (sSup) is a well-defined operation. The trivial upper bound is the total number of pairs of points, (n2)\binom{n}{2}.Source says openFormalized
#97Does every convex polygon have a vertex with no other 4 vertices equidistant from it?Source says falsifiableFormalized
#107Let f(n)f(n) be minimal such that any f(n)f(n) points in R2ℝ^2, no three on a line, contain nn points which form the vertices of a convex nn-gon. Prove that f(n)=2n−2+1f(n) = 2^{n-2} + 1.Source says falsifiableFormalized
#216No statement retained — open to read what the source holdsSource says disprovedNo formal declaration
#651No statement retained — open to read what the source holdsSource says disprovedNo formal declaration
#660No statement retained — open to read what the source holdsSource says openNo formal declaration
#838No statement retained — open to read what the source holdsSource says openNo formal declaration
#956No statement retained — open to read what the source holdsSource says openNo formal declaration
#982If nn distinct points in R2\mathbb{R}^2 form a convex polygon then some vertex has at least ⌊n2⌋\lfloor\frac{n}{2}\rfloor different distances to other vertices.Source says falsifiableFormalized