Question

( 4 la n x 3 la n +1 +12 la n+1 - 6 la n x 2 la n +1) : 13

Answer 1

4 ⁿ x 3ⁿ⁺ ¹  + 12ⁿ ⁺¹ - 6ⁿ x 2ⁿ⁺¹

= ( 4 x 3)ⁿ x 3 + 12ⁿ x 12 - ( 6 x 2 )ⁿ x 2  =

= 12ⁿ x 3 + 12ⁿ x 12 - 12ⁿ x 2  =

= 12ⁿ x ( 3 + 12 - 2 ) =

= 12ⁿ x 13   → divizibil cu 13 → c.c.t.d