Note on Euler’s 𝜑-function

1922/01/01 by R. D. Carmichael · 40 citations
Mathematics · #Mathematics and Applications #Mathematics #Euler's formula #Function (biology) #Applied mathematics #Pure mathematics #Mathematical analysis #Biology

paper · pdf · doi:10.1090/s0002-9904-1922-03504-5

published in Bulletin of the American Mathematical Society 28(3), 109-110 (American Mathematical Society)

openalex publication_date 1922/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

Two correspondents have recently called my attention to the fact that the supposed proof of the following theorem, which I gave some years ago,* is not adequate : THEOREM I. For a given number n the equation <p(x) = n either has no solution or it has at least two solutions.

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• Carmichael's totient function conjecture [wikipedia]