Answers are grounded in this paper and cite their sources.
This record provides the preprint "Lehmer’s Totient Problem and a Prime-Cost Pivot Method". It resolves Lehmer’s totient problem by proving that no composite integer n satisfies phi(n) | (n − 1). The proof combines a prime-cost pivot inequality ruling out the large-parameter regime with a finite-range, machine-checkable certificate for the remaining window, verified by deterministic scripts. Companion materials (code and certificate artefacts) are provided in the associated companion repository for this record.
No takes yet. Share an insight, caveat, or question.
Daniel Sautot (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: