Question

A = 3 la puterea 2n+5 × 7 la puterea n - 63 la puterea n+1 - 3 la puterea 2n+1 × 7 la puterea n+2 sa se divida cu 33

Answer 1

.....................................................................

Answer 2

A = 3²ⁿ⁺⁵ x 7ⁿ - 63ⁿ⁺¹ - 3²ⁿ⁺¹ x 7ⁿ⁺²

A = 3²ⁿ x 3⁵ x 7ⁿ -  ( 9 x 7 )ⁿ⁺¹ - 3²ⁿ x 3 x 7ⁿ x 7²

A = ( 3²ⁿ x 7ⁿ ) x 3⁵ - 9ⁿ x 9 x 7ⁿ x 7 - ( 3²ⁿ x 7ⁿ ) x ( 3 x 7²)

A =  ( 3²ⁿ x 7ⁿ ) x 3⁵ - 3²ⁿ x 9 x 7ⁿ x 7 - ( 3²ⁿ x 7ⁿ ) x ( 3 x 7²)

A = ( 3²ⁿ x 7ⁿ ) x ( 3⁵ - 9 x 7 - 3 x 7² )

A = ( 9 x 7)ⁿ x ( 243 - 63 - 147 )

A = 63ⁿ x ( 180 - 147 )

A = 63ⁿ x 33 →  divizibil cu 33