Repdigits as Euler functions of Lucas numbers

Abstract

We prove some results about the structure of all Lucas numbers whose Euler function is a repdigit in base 10. For example, we show that if Ln is such a Lucas number, then n < 10111 is of the form p or p2, where p3 | 10p-1 -1.

Keywords

• fibonacci numbers
• lucas numbers
• applications of linear forms in logarithms
• primary 11b39
• secondary 11d61