Explicație pas cu pas:
[tex]{10}^{n + 1} - {10}^{n} = {10}^{n} \cdot (10 - 1) = {(2 \cdot 5)}^{n} \cdot 9 = {2}^{n} \cdot {5}^{n} \cdot 9[/tex]
[tex]{5}^{n + 1} + 4 \cdot {5}^{n} = {5}^{n} \cdot (5 + 4) = {5}^{n} \cdot 9[/tex]
[tex]{2}^{n} \cdot \red{ {5}^{n} \cdot 9} \ \ \vdots \ \ \red{ {5}^{n} \cdot 9}[/tex]
=>
[tex]( {10}^{n + 1} - {10}^{n}) \ \ \vdots \ ({5}^{n + 1} + 4 \cdot {5}^{n})[/tex]
q.e.d.
