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\(\varphi(F_{11})=88\). (English) Zbl 1132.11003

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 \((n,m,a)= (11,2,8)\).

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11D99 Diophantine equations
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