## Problem 1

a) Compare the numbers $x, y, z$ knowing that:

$$
\begin{aligned}
& x=(111+222+333+\cdots+888): 111+64 \\
& y=\left(2^{10}-2^{9}\right)\left(2^{9}-2^{8}\right)\left(2^{8}-2^{7}\right): 2^{24} \\
& z=2014^{2}-2014-2013
\end{aligned}
$$

b) Calculate the remainder of the division of the number $n=456^{2014}+4$ by 10.
## Problem 1

a) $x=100$

(1p) ; $y=1$

(1p); $\quad \mathrm{z}=2013^{2}$

(1p); $\quad \mathrm{y}<\mathrm{x}<\mathrm{z}$

(1p)

u.c. $\left(456^{2014}\right)=6$

(1p); n divisible by 10

(1p); $\mathrm{r}=0$

(1p)