Question

aratati ca A=12^n×24+3^(n+²)×4^(n+¹)+2^(n+³)×6^n este divizibil cu 17

Answer 1

=(2^2 x3)^n x24 +3^(n+2) x(2^2)^(n +1) +2^(n+3) x(2x3)^n=
2^2n x3^n x24 +3^(n+2) x2^(2n +2) +2^(2n+3) x3^n=
2^2n x3^n x(24+9x4 +8)=68 x2^2n x3^n
68=17x4
Deci A se divide cu 17