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PreprintarXiv licencearXiv

Distinct Consecutive Products

  • Przemek Chojecki
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Abstract

We prove that there is a density-one set of positive integers for which the products of all distinct consecutive blocks are distinct, answering a question of Erdős and Graham. The construction retains or rejects entire interiors of consecutive-prime gaps and is therefore stable under passage to longer prefixes. Uniform affine-curve estimates control the witnesses with no previous rejected gap, and a scale-contracting forest controls every remaining witness unconditionally.

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Cite

BibTeXRIS
BibTeX
@misc{chojecki2026distinct,
  title = {{Distinct Consecutive Products}},
  author = {Przemek Chojecki},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17543},
  eprint = {2609.17543},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17543},
}
RIS
TY  - UNPB
TI  - Distinct Consecutive Products
AU  - Przemek Chojecki
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.17543
UR  - https://arxiv.org/abs/2609.17543
AB  - We prove that there is a density-one set of positive integers for which the products of all distinct consecutive blocks are distinct, answering a question of Erdős and Graham. The construction retains or rejects entire interiors of consecutive-prime gaps and is therefore stable under passage to longer prefixes. Uniform affine-curve estimates control the witnesses with no previous rejected gap, and a scale-contracting forest controls every remaining witness unconditionally.
ER  -