Positive integer solutions of an equation involving Euler, generalized Euler, and Smarandache functions
Year: 2025
Type: conference-paper
Abstract: This study investigates the positive integer solutions of an equation involving the Smarandache function. The equation is given by tφ(n) = φ 2 (n) + S(n 16), where φ(n) represents the Euler function, φ e (n) represents the generalized Euler function with e as a positive integer, and S(n) represents the Smarandache function. The solutions of this equation are discussed, and it is proven that the equation only has positive integer solutions when t = 1, 2, 3, 6, 7, 9, 12, 17, 18, 19. Furthermore, all positive integer solutions of the equation are provided.
Authors: Lianxia Jiang, Li Wang, Sibao Zhang, Jiangang Tang
Institution: Kashi University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408039146