Question

Determinati ultima cifra a numerelor: 4^12+5^23+6^10
10^12+9^12+*^12
1^4+265+3^6+4^7+5^8+6^9+7^10
123^45+3.232^127+1.478.529^2.481+5.678.413^14.568

Answer 1

a = 4^12 + 5^23 + 6^10    Uc(4^12) = 6     (4^1 =4, 4² =16, 4³  = ..4) Uc a lui 5 la orice putere este 5; Uc(6^n) = 6 ⇒ Uc(a) = Uc(6+5+6) =7

b=10^12 + 9^12 + 8^12 ⇒ Uc(b) = Uc(0+1+6) = 7

c= 1^4 + 2^5 +3^6 + 4^7 + 5^8 + 6^9 + 7^10=Uc(1+2+9+4+5+6+9) =Uc(36) = 6

d = 123^45 + 3232^127 + 1478529^2481 + 5678413^14568⇒  Uc(d) = Uc(3^5) + Uc[2^(124+3)] + Uc[9^(2480+1)] + Uc[3^4] = Uc(3+8+9+1) = Uc(21) = 1