Es seien ${\displaystyle {}a}$ und ${\displaystyle {}n}$ natürliche Zahlen mit ${\displaystyle {}n\geq 2}$. Es sei

${\displaystyle {}a=\sum _{i=0}^{\ell }a_{i}n^{i}\,}$

die Darstellung von ${\displaystyle {}a}$ zur Basis ${\displaystyle {}n}$ (also mit ${\displaystyle {}0\leq a_{i}<n}$).

${\displaystyle {}k}$

${\displaystyle {}n-1}$

${\displaystyle {}a}$

${\displaystyle {}k}$

${\displaystyle {}\sum _{i=0}^{\ell }a_{i}}$

${\displaystyle {}k}$