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A result of Adamczewski implies the existence of constants $c^{(m)}$ such that the $m$-bonacci word is $c^{(m)}$-balanced, i.e., numbers of letter $a$ occurring in two factors of the same length differ at most by $c^{(m)}$ for any letter $a\\in \\mathcal{A}$. The constants $c^{(m)}$ have been already determined for $m=2$ and $m=3$. 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