# Article

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Keywords:
balancing number; repdigit; Diophantine equations; linear form in logarithms
Summary:
The sequence of balancing numbers \$(B_{n})\$ is defined by the recurrence relation \$B_{n}=6B_{n-1}-B_{n-2}\$ for \$n\geq 2\$ with initial conditions \$B_{0}=0\$ and \$B_{1}=1.\$ \$B_{n}\$ is called the \$n\$th balancing number. In this paper, we find all repdigits in the base \$b,\$ which are sums of four balancing numbers. As a result of our theorem, we state that if \$B_{n}\$ is repdigit in the base \$b\$ and has at least two digits, then \$(n,b)=(2,5),(3,6) \$. Namely, \$B_{2}=6=(11)_{5}\$ and \$B_{3}=35=(55)_{6}.\$
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