[tex]\displaystyle{ A = 2^{2012} + 2^{2011} + 2^{2010} + 2^{2009} }[/tex]
[tex]\displaystyle{ A = 2^{2009} \cdot (2^{3} + 2^{2} + 2 + 1) }[/tex]
[tex]\displaystyle{ A = 2^{2009} \cdot (8 + 4 + 2 + 1) }[/tex]
[tex]\displaystyle{ A = 2^{2009} \cdot 15 \ \vdots \ 15 }[/tex]
q.e.d.
[tex]\displaystyle{ B = 3^{999} + 3^{1001} + 3^{1003} }[/tex]
[tex]\displaystyle{ B = 3^{999} \cdot (1 + 3^{2} + 3^{4}) }[/tex]
[tex]\displaystyle{ B = 3^{999} \cdot (1 + 9 + 81) }[/tex]
[tex]\displaystyle{ B = 3^{999} \cdot 91 \ \vdots \ 91 }[/tex]
q.e.d.
PS: Rezolvati-le se scrie cu cratima!
