Repdigits as sums of three balancing numbers

Mahadi Ddamulira (1)

1 TU Graz - Graz University of Technology [Graz]

Let $ \{B_n\}_{n \ge 0} $ be the sequence of Balancing numbers defined by $B_0 = 0, ~B_1 = 1$, and $B_{n+2} = 6B_{n+1} − B_n$ for all $n \ge 0$. In this paper, we find all repdigits in base $10$ which can be written as a sum of three Balancing numbers.

Mots clés: Linear forms in logarithms; Repdigits; Balancing numbers

Domaines: Théorie des nombres [math.NT]

Mahadi Ddamulira. Repdigits as sums of three balancing numbers. Mathematica Slovaca, 2020, 70 (3), pp.557-566. ⟨10.1515/ms-2017-0371⟩. ⟨hal-02405969v2⟩