bibkey: miska2016derangements authors: Piotr Miska year: 2016 title: Arithmetic Properties of the Sequence of Derangements and its Generalizations doi: 10.1016/j.jnt.2015.11.014 claim: The paper records the identity v_2(D_n) = v_2(n-1) for derangement numbers and studies perfect-power equations for the sequence. strata_touched:
- D5/S3/Arith/Derangements/DerangementTwoAdicValuation license: citation-only triage: anchor
Arithmetic Properties of the Sequence of Derangements and its Generalizations
Piotr Miska studies arithmetic properties of the derangement sequence. The
paper explicitly records the identity v_2(D_n) = v_2(n - 1). Its discussion
of perfect powers includes Proposition 31, which treats the equation
D_n = p^k with a fixed prime base.
The repository theorem is independently derived from Mathlib’s recurrence and parity facts. This note supplies mathematical context rather than attestation for the Lean proof. In particular, the repository’s natural-base statement also allows composite and zero bases and is not attributed verbatim to the paper.
Search log
- 2026-09-10: Checked arXiv
1508.01987for the displayed binary-valuation identity and the scope of Proposition 31. - 2026-09-10: Verified the journal metadata and DOI as Journal of Number
Theory 162 (2016), DOI
10.1016/j.jnt.2015.11.014.
Verified locator
- Preprint: https://arxiv.org/abs/1508.01987
- DOI: https://doi.org/10.1016/j.jnt.2015.11.014