Question

Arătați că acest număr e divizibil cu 108​

Answer 1

3^(2n+3)*4^(2n+3)-2^(2n+1)*6^(2n+3)

=(3*4)^(2n+3)-2^(2n+1)*6^(2n+1)*6²

=12^(2n+3)-(2*6)^(2n+1)*6²

=12^(2n+1)*12²-12^(2n+1)*6²

=12^(2n+1)*(12²-6²)

=12^(2n+1)*(144-36)

=12^(2n+1)*108 ⋮ 108

Kawaiimath