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2 published collections

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Published collections

Collection names qualify local identifiers; inclusion does not determine scientific truth.

Erdős Problems
The source-owned Erdős problem catalogue, with status, evidence, Results, and retained formalizations.
1,217 numbered Problems
Formal Conjectures
A bounded rights-reviewed subset of exact research-open Lean declaration occurrences from the upstream collection.
7 published formalizations

Problems to explore

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Erdős Problems

Suppose $n$ points in $\mathbb{R}^2$ determine a convex polygon and the set of distances between them is $\{u_1,\ldots,u_t\}$ . Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then $\sum_i f(u_i)^2 \ll n^3.$
proved (Lean)4 formal declarations1 reviewed Resultvia Formal Conjectures
What is the largest $A\subseteq\{1,\dots,N\}$ such that all subset sums $\sum_{n\in S}1/n$ (over $S\subseteq A$ ) are distinct?
solved6 formal declarations1 reviewed Resultvia Erdős Problems
If $A\subseteq\{1, ..., N\}$ with $|A| = n$ is such that the subset sums $\sum_{a\in S}a$ are distinct for all $S\subseteq A$ then $N \gg 2 ^ n.$
open8 formal declarationsvia Formal Conjectures

Formal Conjectures

For every integer $x \ge 2$ there exists a prime between $x(x-1)$ and $x^2$ .
Wikipedia · formalized occurrence
For every integer $x \ge 2$ there exists a prime between $x^2$ and $x(x+1)$ .
Wikipedia · formalized occurrence
Oppermann's Conjecture
Wikipedia · formalized occurrence

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