Question

Arata ca numarul
a=1+5+5 la puterea a 2 a+...5 la puterea 2013 este divizibil cu 6 plss

Answer 1

[tex]A=5^{0}+5^{1}+5^{2}+...+5^{2013}(2014\ termeni)\\5^{0}+5^{1}=1+5=6\\ Grupam\ cate\ doi\ termeni\\Vor\ fi\ necesare\ \frac{2014}{2}=1007\ paranteze\\A=(5^{0}+5^{1})+(5^{2}+5^{3})+....+(5^{2012}+5^{2013})\\ A=5^{0}*6+5^{2}*6+...+5^{2012}*6\\Dam\ factor\ comun\ 6\\ A=6*(5^{0}+5^{2}+...+5^{2012})\\A\ divizibil\ cu\ 6[/tex]