Question

Demonstrati ca: a) ( 2 la puteria 33- 2 la puteria31) estemultiplu de 3 b) 5 este divizorul lui (2 la putera 20 + 3 la putreria22)

Answer 1

   
[tex]a)~~~2^{33}-2^{32} = 2^{31}(2^2-1)=2^{31}(4-1) = \boxed{3\times 2^{31}~\vdots~3}\\\\ b)~~~3^{20}+3^{22}=3^{20}(1+3^2)=3^{20}(1+9) = \boxed{10\times 3^{20}~\vdots~5}\\\\ \text{Am corectat greseala din enuntul tau la b).}\\ \text{Am scris }3^{20}~\text{in loc de } 2^{20} [/tex]