Let α be an irrational number with 0<α<1, and draw a circle in the plane whose circumference has length 1. Given any integer n≥3, define a sequence of points P1,P2,…,Pn as follows. First select any point P1 on the circle, and for 2≤k≤n define Pk as the point on the circle for which the length of arc Pk−1Pk is α, when travelling counterclockwise around the circle from Pk−1 to Pk. Suppose that Pa and Pb are the nearest adjacent points on either side of Pn. Prove that a+b≤n. floor functioninductionanalytic geometryirrational numberAMCUSAJMO