Question

A=3 la 2n +1×5 la 3n +2-9 la n+1×5 la 3n+1.Arătați că A se împarte la 90

Answer 1

A = 3^2n+1 × 5^3n+2 - 9^n+1 × 5^3n+1

A = 3^2n × 3^1 × 5^3n × 5^2 - 9^n×9^1 ×5^3n × 5^1

A = 9^n × 5^3n × 3 × 25 - 9^n × 5^3n × 9 × 5

A = 5^3n × ( 9^n × 75 - 9^n × 45)

A = 5^3n × 9^n × ( 75 - 45 )

A = 5^3n × 9^n × 30