4. On $\mathbb{R}$ we define the law $x * y=5 x y+5(x+y)+4, x, y \in \mathbb{R}$.
a) Is $(\mathbb{R}, *)$ a group?

b) Calculate $(-2014) *(-2013) * \ldots * 2013 * 2014$;

c) Determine the last 2006 digits of the number $1 * 2 * \ldots * 2014$.
a) $x * y=5(x+1)(y+1)-1$ associative, commutative, $e=-\frac{4}{5}, U(\mathbb{R})=\mathbb{R}-\{-1\}$. ................................................................................... 2 points
b) $x *(-1)=-1 \Rightarrow(-2014) *(-2013) * \ldots * 2013 * 2014=-1$ .2 points
c) $1 * 2 * \ldots * 2014=\underbrace{5^{2013} 2015!}_{\vdots 10^{2005}}-1 \Rightarrow 1 * 2 * \ldots * 2014$ ends in 2005 nines preceded by the digit 4