Erdős problem 107

Let $f(n)$ be minimal such that any $f(n)$ points in $ℝ^2$ , no three on a line, contain $n$ points which form the vertices of a convex $n$ -gon. Prove that $f(n) = 2^{n-2} + 1$ .

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

107.lean

Retained formal statement1 of 7

Let $f(n)$ be minimal such that any $f(n)$ points in $ℝ^2$ , no three on a line, contain $n$ points which form the vertices of a convex $n$ -gon. Prove that $f(n) = 2^{n-2} + 1$ .

FormalConjectures/ErdosProblems/107.leanErdos107.erdos_1071 lineExact file

1sorry ↔ ∀ n ≥ 3, Erdos107.f n = 2 ^ (n - 2) + 1

OpenStatement only, no proof

Source providers

Erdős Problems1
locator only
Formal Conjectures7
statement retained
VibeMathed0
not observed here
PLBY Lean proofs0
not observed here
Jayyhk Erdős Lean0
not observed here
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki0
not observed here
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 107.lean7