E.502. Determinați ultimele 444 cifre ale numărului a=22026−22020−22019.a=2^{2026} - 2^{2020} - 2^{2019}.a=22026−22020−22019.
Răspuns: 6000.6000.6000.
a=22019(27−2−1)=22019⋅125=22016⋅(2⋅5)3.a=2^{2019}(2^7-2-1) = 2^{2019} \cdot 125=2^{2016} \cdot (2 \cdot 5)^3.a=22019(27−2−1)=22019⋅125=22016⋅(2⋅5)3. a=22016⋅103Uc(22016)=Uc(24)=6}⇒U4c(a)=6,0,0,0. \begin{rcases} a=2^{2016} \cdot 10^3 \\ U_c(2^{2016}) = U_c(2^4)=6 \end{rcases} \Rightarrow \boxed{U_{4c}(a)=6,0,0,0}. a=22016⋅103Uc(22016)=Uc(24)=6}⇒U4c(a)=6,0,0,0.