Question 19
Let $n \in \mathbb{N}$, $n \ge 2$. Consider the equation:
$$
\{x\} + \{2x\} + \dots + \{nx\} = [x] + [2x] + \dots + [2nx].
$$
a) Solve the equation in $\mathbb{R}$ for $n = 2$.
b) Prove that the equation has at most two real solutions for any $n \ge 2$.
$$
\{x\} + \{2x\} + \dots + \{nx\} = [x] + [2x] + \dots + [2nx].
$$
a) Solve the equation in $\mathbb{R}$ for $n = 2$.
b) Prove that the equation has at most two real solutions for any $n \ge 2$.