Luca, Florian; Mignotte, Maurice \(\varphi(F_{11})=88\). (English) Zbl 1132.11003 Divulg. Mat. 14, No. 2, 101-106 (2006). The solution to the Diophantine equation \[ \varphi(F_n)= a{10^m- 1\over 10-1}= \max,\quad a\in \{1,\dots, 0\} \] with the Euler function \(\varphi\) and the \(n\)th Fibonacci number \(F_n\) is given by \((n,m,a)= (11,2,8)\). Reviewer: Joachim Piehler (Merseburg) Cited in 3 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11D99 Diophantine equations Keywords:Fibonacci numbers; Diophantine equation PDFBibTeX XMLCite \textit{F. Luca} and \textit{M. Mignotte}, Divulg. Mat. 14, No. 2, 101--106 (2006; Zbl 1132.11003) Full Text: EuDML