## Chèfiath A. Adegbindin, Alain Togbé

*Can a Lucas number be a sum of three repdigits?*

Comment.Math.Univ.Carolin. 61,3 (2020) 383-396.**Abstract:**We give the answer to the question in the title by proving that \begin{equation*} L_{18} = 5778 = 5555 + 222 + 1 \end{equation*} is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.

**Keywords:** Pell equation; repdigit; linear forms in complex logarithms

**DOI:** DOI 10.14712/1213-7243.2020.028

**AMS Subject Classification:** 11A25 11B39 11J86

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