Question

Arătați ca a= 14^n + 2^n+2 × 7^n + 2^n × 7^n+2 este divizibil cu 27, oricare ar fi n nr natural.

Answer 1

a=14^n+2^n+2*7^n+2^n*7^n+2=
=14^n+2^n*2^2*7^n+2^n*7^n*7^2=
=14^n+14^n*2^2+14^n*7^2=
=14^n*(1+2^2+7^2)=
=14^n*54=
=14^n*2*27  }  =>27|14^n*2*27=>27|a
        27|27    }