Question

FIe n un nr natural . determinati ultima cifra a nr a si b , unde a= 1989 ^ 2n +1 + 1997^4n+1 + 2004 ^2003 + 2003 ^ 2004 si b= 2004^n + 2005 ^n + 2006 ^ n

Answer 1

U(a) = U( 1989 ^ 2n +1 + 1997^4n+1 + 2004 ^2003 + 2003 ^ 2004 )=\
        = U(9^2n *9 +7^4n *7 +4^2000 *4^3 +3^2004)=
        =U(1*9+1*7+6*4+1)=
        =U(1+7+4+1)
        =3

U(b)=U(2004^n + 2005 ^n + 2006 ^ n)=
       =U(4^n+5+6)=
  U(4^n) =4 daca n este impar si 6 daca n este par =>
=> U(4^n+5+6) = 5 sau 7