Question

Aratati ca 10 la puterea n +314 este divizibil cu 9 pt orice nr nat n

Answer 1

   
[tex]\displaystyle \\ 10^n + 314 = \\ \\ =1\underbrace{0000\hdots 0000}_{\text{n zerouri}} + 314 = \\ \\ =1\underbrace{0000\hdots 0}_{\text{n-3 zerouri}}314 \\ \\ \text{Suma cifrelor numarului este: } \\ \\ 1 + 0(n-3) + 3+1+4 = 1+0+3+1+4 = \boxed{9} \\ \\ \Longrightarrow ~~~ (10^n + 314)~\vdots~9[/tex]