Deng, Guilin; Liao, Qunying The solvability of the equation \({\varphi_e} (n) = 2^{t\omega (n)}\). (Chinese. English summary) Zbl 1463.11006 J. Sichuan Norm. Univ., Nat. Sci. 43, No. 2, 187-201 (2020). Summary: By using elementary methods and properties of the generalized Euler functions, this paper studies the solvability of the equation \({\varphi_e} (n) = 2^{t\omega (n)}\) for the case \(e \in \{2, 3, 4, 6\}\), and then gives positive integer solutions under given conditions. MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11B68 Bernoulli and Euler numbers and polynomials 11Y70 Values of arithmetic functions; tables Keywords:generalized Euler function equation; positive integer solution PDFBibTeX XMLCite \textit{G. Deng} and \textit{Q. Liao}, J. Sichuan Norm. Univ., Nat. Sci. 43, No. 2, 187--201 (2020; Zbl 1463.11006) Full Text: DOI