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Carmichael's Conjecture | Synapse

March 27, 2026Open Access

Carmichael's Conjecture

Key Points

To prove that every value of Euler's totient function appears at least twice among integers.
Theoretical proof derived within number theory frameworks.
Analysis of the distribution of Euler's totient function values.
Confirmed that no integer value of Euler's totient function is unique.
Established connections to existing theories in number theory.

Abstract

Preprint v1 — A proof that no value of Euler's totient function is taken exactly once. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings. Author: Joseph Keen Affiliation: Phoenix Quantum Labs LLC

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Cite This Study

Joseph R. Keen (Wed,) studied this question.

synapsesocial.com/papers/69c620d515a0a509bde196bb https://doi.org/https://doi.org/10.5281/zenodo.19216569

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