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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
With Repository-reviewed evidence2 / 1,217
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Problems

9 Problems

SelectNumberQuestionOpen
#143Does this imply that lim inf⁡∣A∩[1,x]∣x=0? \liminf \frac{|A \cap [1,x]|}{x} = 0? Source says openFormalized
#164A set A⊂NA\subset \mathbb{N} is primitive if no member of AA divides another. Is the sum ∑n∈A1nlog⁡n\sum_{n\in A}\frac{1}{n\log n} maximised over all primitive sets when AA is the set of primes?Source says proved (Lean)Formalized
#486For each n∈Nn \in \mathbb{N} choose some Xn⊆Z/nZX_n \subseteq \mathbb{Z}/n\mathbb{Z}. Let B={m∈N:∀n,m≢x(modn) for all x∈Xn}B = \{m \in \mathbb{N} : \forall n, m \not\equiv x \pmod{n} \text{ for all } x \in X_n\}. Must BB have a logarithmic density?Source says openFormalized
#858No statement retained — open to read what the source holdsSource says solvedNo formal declaration
#872Each move claims exactly one pool element, so the minimax value never exceeds the number of already claimed elements plus the number of still unclaimed elements.Source says openFormalized
#882No statement retained — open to read what the source holdsSource says solvedNo formal declaration
#892No statement retained — open to read what the source holdsSource says openNo formal declaration
#1196Is it true that, for any xx, if A⊂[x,∞)A\subset [x,\infty) is a primitive set of integers (so that no distinct elements of AA divide each other) thenUnparsed notation: \sum_{a\in A}\frac{1}{a\log a}< 1+o(1),where the o(1)o(1) term →0\to 0 as x→∞x\to \infty? -Source says proved (Lean)Formalized
#1217No statement retained — open to read what the source holdsSource says provedNo formal declaration