Question Number 196672 by Rasheed.Sindhi last updated on 29/Aug/23
$${Find}\:{all}\:\Omega\overline {={abcdef}\:\:},\:{such}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{abcdef}={abc}+{def} \\ $$
Commented by Rasheed.Sindhi last updated on 29/Aug/23
$${Q}#\mathrm{196659} \\ $$
Answered by Rasheed.Sindhi last updated on 30/Aug/23
$${abcdef}={abc}+{def} \\ $$$${abcdef}−{abc}={def} \\ $$$${abc}\left({def}−\mathrm{1}\right)={def} \\ $$$${abc}=\frac{{def}}{{def}−\mathrm{1}}\:\:\:\:\Rightarrow\:\left({def}−\mathrm{1}\right)\mid\:{def}\Rightarrow{def}−\mathrm{1}=\mathrm{1} \\ $$$$\Rightarrow{def}=\mathrm{2} \\ $$$$\begin{cases}{{d}=\mathrm{2},{e}=\mathrm{1},{f}=\mathrm{1}}\\{{d}=\mathrm{1},{e}=\mathrm{2},{f}=\mathrm{1}}\\{{d}=\mathrm{1},{e}=\mathrm{1},{f}=\mathrm{2}}\end{cases} \\ $$$${def}=\mathrm{211},\mathrm{121},\mathrm{112} \\ $$$${abc}=\frac{{def}}{{def}−\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{1}}=\mathrm{2} \\ $$$${abc}=\mathrm{211},\mathrm{121},\mathrm{112} \\ $$$$\Omega=\overline {{abcdef}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{211211},\mathrm{211121},\mathrm{211112}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{121211},\mathrm{121121},\mathrm{121112}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{112211},\mathrm{112121},\mathrm{112112} \\ $$
Commented by Tawa11 last updated on 29/Aug/23
$$\mathrm{Long}\:\mathrm{time}\:\mathrm{sir}. \\ $$
Commented by Rasheed.Sindhi last updated on 30/Aug/23
$${Yes}\:{miss},\:{nowadays}\:{I}\:{rarely}\:{can} \\ $$$$\:{share}\:{any}\:{posts}\:{and}\:{you}\:{also}\:{less} \\ $$$$\:{participate}! \\ $$$${Anyway}\:{thanks}\:{miss}. \\ $$