Question

gasiti n apartine lui N, daca 13×13 la puterea 3×13 la puterea 5× .....×13 la puterea 13= 13 la puterea n la a doua

Answer 1

[tex]13*13^3*13^5*....13^{13}=(13^n)^2\\ 13^{1+3+5+....+13}=13^{n}^{2}\\ Luam\ suma\ separat\\ 1+3+5+...+13=\\ 1+2+3+...+13-2-4-...-12=\\ \frac{13*14}{2}-2(1+2+3+..+6)=\\ 13*7-2*\frac{6*7}{2}=\\ 13*7-6*7=\\ 7(13-6)=7^2\\ 13^7^2=13^n^2\\ n^2=7^2=\ \textgreater \ n=7[/tex]