Question

A=2^n+1x3^2n+2^nx9^n+1. Demonstati ca A divizibil cu 11

Answer 1

A=2^n+1x3^2n+2^nx9^n+1=2·2^n·3^2n+9·2^n·9^n=2·2^n·3^2n+9·2^n·(3²)^n= =2·2^n·3^2n+9·2^n·3^2n=2^n·3^n(2+9)=11·2^n·3^n care este divizibil cu 11