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Erdős problem 331

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Let A,B⊆NA,B\subseteq \mathbb{N} such that for all large NN∣A∩{1,…,N}∣≫N1/2\lvert A\cap \{1,\ldots,N\}\rvert \gg N^{1/2}and∣B∩{1,…,N}∣≫N1/2.\lvert B\cap \{1,\ldots,N\}\rvert \gg N^{1/2}. Is it true that there are infinitely many solutions to a1−a2=b1−b2≠0a_1-a_2=b_1-b_2\neq 0 with a1,a2∈Aa_1,a_2\in A and b1,b2∈Bb_1,b_2\in B?

Erdős Problems records this as disproved (Lean).

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How far the record reaches4 of 6 stages
  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal2 retained
  4. Resolutiondisproved (Lean)
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
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Where the source files it639 share a topic
Number Theory576Additive Combinatorics102
Erdős problem 321accepted
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