Kaidireya, Nuermaimaiti; Zhang, Sibao Discussion of solutions of an equation on the number-theoretic function \(\varphi(m)\). (Chinese. English summary) Zbl 1463.11107 Pure Appl. Math. 36, No. 2, 229-238 (2020). Summary: Let \(\varphi(m)\) be an Euler function, where \(m\) is a positive integer. The solvability of the equation \(\varphi(xyz) = 7(\varphi(x) + \varphi(y) + \varphi(z))\) containing the Euler function \(\varphi(m)\) was discussed. By using elementary methods and the properties of the Euler function \(\varphi(m)\), all 87 sets of positive integer solutions of the equation were given. MSC: 11D72 Diophantine equations in many variables 11D45 Counting solutions of Diophantine equations Keywords:Euler function \(\varphi(m)\); elementary method; positive integer solution PDFBibTeX XMLCite \textit{N. Kaidireya} and \textit{S. Zhang}, Pure Appl. Math. 36, No. 2, 229--238 (2020; Zbl 1463.11107) Full Text: DOI