Perfect numbers, Wieferich primes and the solutions of binom2nn≡ 2ⁿ bmod n

@misc{guedes2026perfect,
  title = {{Perfect numbers, Wieferich primes and the solutions of $\binom2nn\equiv 2^n \bmod n$}},
  author = {Gabriel Guedes and Ricardo Machado},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03091},
  eprint = {2609.03091},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03091},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Perfect numbers, Wieferich primes and the solutions of binom2nn≡ 2^n bmod n
AU  - Gabriel Guedes
AU  - Ricardo Machado
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03091
UR  - https://arxiv.org/abs/2609.03091
AB  - In this article we focus on the solutions of a congruence equation: binom2nn≡ 2^n bmod n. Using the main result of this article and the SageMath software, we improve largely the number of known solutions. Furthermore, we prove that some famous numbers like even perfect numbers and Wieferich primes are connected to solutions of this equation.
ER  -