Question

Demonstrati ca nr A=63 la puterea n+7 la puterea n+1*3 la puterea 2n+1 -21 la puterea n*3 la puterea n+2, n apartine N este divizibil cu 13.

Answer 1

[tex]A=63^n+7^{n+1}\cdot3^{2n+1}-21^n\cdot 3^{n+2}\\ A=63^n+7^n\cdot7\cdot9^n\cdot3-21^n\cdot3^n\cdot9\\ A=63^n+63^n\cdot21-63^n\cdot 9\\ A=63^n(1+21-9)\\ A=63^n\cdot 13\ \vdots\ 13\ \forall n\in N[/tex]