Question

aratati ca numarul N=2^2n+1 ×5^n+2 -4n+1 ×5^n ×10-2^2n+4 ×5^n divizibil cu 24

Answer 1

N=2^(2n+1) ×5^(n+2) -4^(n+1) ×5^n ×10-2^2n+4 ×5^n divizibil cu 24

N=2^(2n+1) ×5^(n+2) -2^(2n+2) ×5^n ×5×2-2^(2n+4) ×5^n =

=2^(2n+1) ×5^(n+2) -2^(2n+3) ×5^n+1 -2^(2n+4) ×5^n =

=2^(2n+1) ×5^n (5^2-2^2 ×5 -2^3 ) =

=2^2n ×5^n (25-20-8) =

=2^2n ×5^n (-3) =

=2^(2n-3) ×5^n (-3)×2³ =

=-2^(2n-3) ×5^n ×24 deci divizibil cu 24