E.510. Determinați ultimele 111111 cifre ale numărului n=52018−52017+2⋅52015+2⋅52014.n=5^{2018}-5^{2017}+2 \cdot 5^{2015} + 2 \cdot 5^{2014}.n=52018−52017+2⋅52015+2⋅52014.
Răspuns: 1100…0⏟9 de 0.11\underbrace{00 \ldots 0}_{\text{9 de 0}}.119 de 000…0.
n=52014(54−53+2⋅5+2)=52014⋅512=52005⋅(5⋅2)9n=5^{2014}(5^4-5^3+2 \cdot 5 + 2) = 5^{2014} \cdot 512 = 5^{2005} \cdot (5 \cdot 2)^9n=52014(54−53+2⋅5+2)=52014⋅512=52005⋅(5⋅2)9. Cu U2c(52005=25)⇒U11c(n)=2500…0⏟9 de 0.U_{2c}(5^{2005} = 25) \Rightarrow \boxed{U_{11c}(n) = 25\underbrace{00 \ldots 0}_{\text{9 de 0}}}.U2c(52005=25)⇒U11c(n)=259 de 000…0.