Elementare Mathematik 1/Gemischte Satzabfrage/29/Aufgabe/Lösung

${\displaystyle {}n}$

${\displaystyle {}k}$

${\displaystyle {}r_{0},r_{1},r_{2},\ldots ,r_{k}}$

${\displaystyle {}0\leq r_{i}\leq 9}$

${\displaystyle {}r_{k}\neq 0}$

${\displaystyle n=0}$

${\displaystyle {}n=\sum _{i=0}^{k}r_{i}10^{i}\,.}$

${\displaystyle {}n}$

${\displaystyle {}m}$

${\displaystyle {}n=\prod _{p}p^{\exp _{p}(n)}}$

${\displaystyle {}m=\prod _{p}p^{\exp _{p}(m)}}$

${\displaystyle {}\operatorname {kgV} (n,m)=\prod _{p}p^{\max {\left({\exp _{p}(n)},{\exp _{p}(m)}\right)}}\,}$

und

${\displaystyle {}\operatorname {ggT} (n,m)=\prod _{p}p^{\min {\left({\exp _{p}(n)},{\exp _{p}(m)}\right)}}\,.}$

${\displaystyle {}a,b}$

${\displaystyle {}b}$

${\displaystyle {}z_{-i}}$

${\displaystyle {}i\in \mathbb {N} }$

${\displaystyle {}r_{-i}}$

${\displaystyle {}i\in \mathbb {N} }$

${\displaystyle {}k\in \mathbb {N} }$

${\displaystyle {}\ell \in \mathbb {N} _{+}}$

${\displaystyle {}\ell <b}$

${\displaystyle {}i>k}$

${\displaystyle {}z_{-i-\ell }=z_{-i}\,}$