AMC 12 2025b Problem 23

Let $S$ be the set of all integers $z > 1$ such that for all pairs of nonnegative integers $(x, y)$ with $x < y < z$, the remainder when $2025x$ is divided by $z$ is less than the remainder when $2025y$ is divided by $z$. What is the sum of the elements of $S$?

\textbf{(A)}~3041 \textbf{(B)}~3542 \textbf{(C)}~3750 \textbf{(D)}~4044 \textbf{(E)}~4319