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PreprintCC BY 4.0arXiv

Distribution of squarefree integers with double congruence conditions

  • Tang Wuji
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Abstract

Given a positive integer M with reduced residue system ΦM, we partition the set of squarefree integers according to some congruence conditions on the number of prime factors in each class ϕ∈ ΦM, and prove two relevant equidsitribution results in this setting. We discover the bias phenomenon in some special cases, and formulate a conjecture with numerical support.

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Cite

BibTeXRIS
BibTeX
@misc{wuji2026distribution,
  title = {{Distribution of squarefree integers with double congruence conditions}},
  author = {Tang Wuji},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16716},
  eprint = {2609.16716},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16716},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Distribution of squarefree integers with double congruence conditions
AU  - Tang Wuji
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16716
UR  - https://arxiv.org/abs/2609.16716
AB  - Given a positive integer M with reduced residue system Φ_M, we partition the set of squarefree integers according to some congruence conditions on the number of prime factors in each class ϕ∈ Φ_M, and prove two relevant equidsitribution results in this setting. We discover the bias phenomenon in some special cases, and formulate a conjecture with numerical support.
ER  -