On the equation F(n^k - 1) = D
We prove that if $F$ is a completely multiplicative function and $k \in \{2, 3\}$ such that the equation $F(n^k - 1) = 1$ holds for every $n \in \mathbb{N}$, $n > 1,$ then $F$ is the identity function. A similar result is proved for the equation $F(n^4 - 1) = 1$ assuming a suitable conjecture concerning prime numbers. The equation $F(n^3 + 1) = 1$ is also studied.
Authors
- Bui Minh Phong (ORCID: https://orcid.org/0000-0001-8371-5279)
- Imre Kátai
- Bui Minh Mai Khanh
Publication Details
- Journal
- Notes on Number Theory and Discrete Mathematics
- Published
- 2025-10-12
- DOI
- https://doi.org/10.7546/nntdm.2025.31.4.718-727
- Primary Topic
- Differential Equations and Boundary Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00