Question

ultima cifrà a nr. 3 la puterea laputerea 2000 +4 la puterea 2000+ 7 la puterea 2000 ?

Answer 1

U(3^2000); 2000:4=500 r=0    U= 3^4=81, U(3^2000)=1
U(4^2000); 2000:2=1000 r=0  U=4^2=16; U(4^2000)=6
U(7^2000); 2000:4=500 r=0    U=7^4; U(7^2000)=1

ultima cifra a sumei=1+6+1=8

Answer 2

Uc=ultima cifra
Uc(3^2000 ) = 1    3^1 = 3; 3² = 9; 3³ = ....7    3^4 = ....1
Uc(4^2000 ) = 6    4^1 = 4; 4²=......6
Uc(7^2000) = 1     7^1 = 7; 7² =....9; 7³ =....3; 7^4 = ....1
Uc =1+6+1
Uc=8