Lucas Numbers Which Are Concatenations of Two Repdigits

Abstract

In this paper, we find all Lucas numbers written in the form c⋯cd⋯d¯, where c⋯cd⋯d¯ is the concatenation of two repdigits in base 10 with c,d∈{0,1,⋯,9}, c≠d and c>0.

Keywords

• Lucas numbers
• concatenations of two repdigits
• logarithmic height
• continued fraction