Question

Demonstrati ca x=4^n×3^2n+1+2^2n+3×9^n divizibil cu 11

Answer 1

x = 4^n × 3^2n+1 + 2^2n+3 × 9^n

x = 2^2n × 3^2n × 3 + 2^2n × 2^3 × 3^2n

x = (2 × 3)^2n × 3 + (2 × 3)^2n × 8

x = 6^2n × 3 + 6^2n × 8

x = 6^2n × ( 3 + 8)

x = 6^2n × 11 divizibil cu 11
_____________________