A Flanking Pattern in a Sum-of-Divisors Congruence
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914212575444992 |
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| author | Kominers, Scott Duke |
| author_facet | Kominers, Scott Duke |
| contents | We consider composite $n$ satisfying the congruence $$n \cdot σ_k(n) \equiv 2 \pmod{ϕ(n)},$$ and show a "flanking" structure: $14$ appears in both $S_{k-1}$ and $S_{k+1}$ whenever certain values of $n$ appear in $S_k$; and, moreover, $14$ is the only (nontrivial) case of this property. Along the way, we derive a new characterization of the $n$ that appear in the sets $S_{k}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Flanking Pattern in a Sum-of-Divisors Congruence Kominers, Scott Duke Number Theory 11A07, 11A25, 11A41 We consider composite $n$ satisfying the congruence $$n \cdot σ_k(n) \equiv 2 \pmod{ϕ(n)},$$ and show a "flanking" structure: $14$ appears in both $S_{k-1}$ and $S_{k+1}$ whenever certain values of $n$ appear in $S_k$; and, moreover, $14$ is the only (nontrivial) case of this property. Along the way, we derive a new characterization of the $n$ that appear in the sets $S_{k}$. |
| title | A Flanking Pattern in a Sum-of-Divisors Congruence |
| topic | Number Theory 11A07, 11A25, 11A41 |
| url | https://arxiv.org/abs/2512.18424 |