# AI provenance: Lehmer's totient problem with fewer than sixteen prime factors

Authors: Deep Bhattacharjee. No AI system is an author or contributor.

## How the work was produced

Deep Bhattacharjee chose the problem, directed the work and takes responsibility for the content. Claude (Anthropic), used through Claude Code, wrote and ran the search programs in Python and PARI/GP, wrote the Lean 4 proofs of the statements that do not depend on a search, drew the figures and drafted the text. The author reviewed and edited the text.

## How the results are checked

Every statement is proved in the text or reduced by hand to a finite computation. Each computation was carried out by two independently written programs, one of which never factors an integer, and both were run on an equation whose fifty-six solutions are known (Appendix A). The statements that need no search are proved in Lean 4. No result rests on an AI output that was not checked in one of these ways. Every reference was checked against its registration record.

## What is not claimed

Lehmer's totient conjecture is not proved. Proposition 9.1 states the assertion equivalent to it, with two constraints on its divisor D.

## Labels given on the Hexagon form

- Text of the contribution: a mix of human-written and AI-generated (to be confirmed by the author).
- Human understanding at submission: some parts, but not all, checked and understood by a human (to be confirmed by the author).

## Where everything is

Release v1.4.0: https://github.com/creelie/eLhmr/releases/tag/v1.4.0. The paper's Data and code availability section makes the same disclosure.