Question

Dau coroana:
2la puterea 44+2la puterea 47+2la puterea 45.

Demonstrati ca
(Ab51+2ab)se divide cu 51

Answer 1

    
[tex]1)~~~2^{44}+2^{47}+2^{45}=2^{44}(1+2^3+2^1) =2^44(1+8+2)=\boxed{11\times 2^{44}} \\ \\ 2) \\ \overline{ab51} + 2 \times \overline{ab}= \\ = 100 \times \overline{ab}+51+ 2 \times \overline{ab}= \\ =100 \times \overline{ab}+2 \times \overline{ab}+51 = \\ = \overline{ab}(100+2)+51 = \\ =102 \times \overline{ab} + 51 = \boxed{51(2 \times \overline{ab} + 1)~ \vdots ~51}~~semnul ~"~\vdots~"~= "divizibil" \\ cctd [/tex]