Question 3
Find all positive integers $k\lt 202$ for which some positive integer $n$ satisfies
$$\left\{\frac n{202}\right\}+\left\{\frac{2n}{202}\right\}+\cdots+\left\{\frac{kn}{202}\right\}=\frac k2.$$
Here $\{x\}$ is the fractional part: the unique real number in $[0,1)$ whose difference from $x$ is an integer.
$$\left\{\frac n{202}\right\}+\left\{\frac{2n}{202}\right\}+\cdots+\left\{\frac{kn}{202}\right\}=\frac k2.$$
Here $\{x\}$ is the fractional part: the unique real number in $[0,1)$ whose difference from $x$ is an integer.