Submitted:
14 January 2026
Posted:
15 January 2026
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Abstract
This paper presents a self-contained proof of Lehmer's Totient Problem. It states that if Euler’s totient function φ(n) divides n-1, then n must be prime. The proof is established by simplifying the structure of the problem and demonstrating that it does not hold for any set of primes.
Keywords:
Lehmer totient problem
; Euler totient
; number theory
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