Question

calculeaza ultima cifra a numarului 2^100 + 3^102 + 4^103 + 5^104

Answer 1

U( 2^100+3^102+4^103+5^104) =

= U(2^4) + U(3^2) + U(4^3) + 5 =

= U(16) + U(9) + U(64) + 5 =

= U(6 + 9 + 4 + 5) =

= U(24) =

= 4

100 : 4 = 25 ==> U(2^100) = U(2^4) = 6

102 : 4 = 25 rest 2==> U(3^102) = U(3^4×25+2) = U(3^2) = 9

103 : 4 = 25 rest 3 ==> U(4^103) = U(4^4×25+3) = U(4^3) = U(64) = 4

U(5^104)
5 la orice putere va avea intotdeauna ultima cifra 5