[tex]\displaystyle{ 2^{50} + 2^{52} = 2^{50} \cdot (1 + 2^{2}) = 2^{50} + (1 + 4) = 5 \cdot 2^{50} }[/tex]
[tex]\displaystyle{ 5^{21} = 5^{20} \cdot 5 }[/tex]
Impartim ambele numere prin 5.
Trebuie comparat:
[tex]\displaystyle{ 5^{20} \ cu \ 2^{50} }[/tex]
[tex]\displaystyle{ 5^{20} = (5^{2})^{10} = 25^{10} }[/tex]
[tex]\displaystyle{ 2^{50} = (2^{5})^{10} = 32^{10} }[/tex]
[tex]\displaystyle{ 25^{10} < 32^{10} \rightarrow 5^{21} < 2^{50} + 2^{52} }[/tex]
Matei
