Explicație pas cu pas:
[tex]{2}^{n + 2} + {2}^{ \red{ \bf n}} = {2}^{2} \cdot {2}^{n} + {2}^{n} = {2}^{n} \cdot (4 + 1) = 5 \cdot {2}^{n}[/tex]
[tex]{4}^{n + 1} + {4}^{n} = 4 \cdot {4}^{n} + {4}^{n} = {4}^{n} \cdot (4 + 1) = 5 \cdot {4}^{n} = 5 \cdot {( {2}^{2} )}^{n} = 5 \cdot {( {2}^{n} )}^{2}[/tex]
atunci:
[tex]5 \cdot {2}^{n} \ \Big| \ 5 \cdot {( {2}^{n} )}^{2}[/tex]
[tex]\implies ({2}^{n + 2} + {2}^{n}) \ \Big| \ ({4}^{n + 1} + {4}^{n})[/tex]
q.e.d.
