Question

Arătați că numarul 1+2+2^2+2^3+2^4+2^5+2^6...…..+2^96+2^97+2^99 se divide cu 15

Answer 1

(1+2+2^2+2^3)+2^4 (1+2+2^2+2^3)+2^5 (1+2+2^2+2^3)+2^6 (1+2+2^2+2^3)+....+2^94(1+2+2^2+2^3)+2^95 (1+2+2^2+2^3)+2^97 (1+2+2^2+2^3)=15 (1+2^4+2^5+2^6+...2^94+2^95+2^96) este divizibil cu 15