Question

demonstrati ca numarul A=63^n+7^n+1x3^n+21^nx3^n+2, n apartine N este divizibil cu 13

Answer 1

[tex]A=63^n+7^{n+1}\cdot 3^n+21^n\cdot 3^{n+2},n\in N\\ A=63^n+7^n\cdot 7\cdot 3^{2n}+21^n\cdot3^n\cdot3 ^2\\ A=63^n+7^n\cdot 9^n\cdot 7+21^n\cdot 3^n\cdot 9\\ A=63^n+63^n\cdot 7+63^n\cdot 9\\ A=63^n(1+7+9)\\ A=63^n\cdot 17 \vdots\ 17\\ Numarul\ nu\ este\ divizibil\ cu\ 13.[/tex]