Question

Aratati ca numarul A= 2²+2⁴+2⁶+...+2³⁰ este divizibil cu 20

Answer 1

[tex]A=2^2+2^4+2^6+2^8+...+2^{30}\\ A=(2^2+2^4)+2^4(2^2+2^4)+....+2^{26}(2^2+2^4)\\ A=(2^2+2^4)(1+2^4+...+2^{26})\\ A=(4+16)(1+2^4+....+2^{26})\\ A=20\cdot (1+2^4+....+2^{26}) \vdots\ 20[/tex]