Răspuns:
4.
a) 2³+2⁴+2⁵=8+16+32=56
b) 2³⁰+2³¹+2³²=2²⁷(2³+2⁴+2⁵)=2²⁷x56 care este divizibil cu 56
c) 2¹+2²+(2³+2⁴+2⁵)+2³(2³+2⁴+2⁵)+ ... +2²⁷(2³+2⁴+2⁵) =
2¹+2²+(1+2³+2⁶+...+2²⁷)(2³+2⁴+2⁵) =
2¹+2²+ A x 56 =
6 + A x 56
deci restul este 6
5.
[tex]a = {2}^{34} + {5}^{2 \times 21} [/tex]
[tex]b = {3}^{3 \times 21 } + {2}^{36} = {2}^{34} \times {2}^{2 } + ( {3}^{3}) ^{21} [/tex]
deci
[tex]a = {2}^{34} + {25}^{21} [/tex]
[tex]b = {2}^{34} \times 4 + {27}^{21} [/tex]
deci
[tex]b > a[/tex]
