USAJMO 2012 Question 4

Let $0\lt \alpha\lt 1$ be irrational. On a circle of circumference 1 choose $P_1$, and define $P_k$ by moving counterclockwise an arc length $\alpha$ from $P_{k-1}$, for $2\le k\le n$, where $n\ge3$. If $P_a,P_b$ are the adjacent points immediately on either side of $P_n$ among these $n$ points, prove $a+b\le n$.

Proposed by Sam Vandervelde (credit in the supplied notes).