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The number that made entry of points

Source: Japan Mathematical Olympiad Finals 1998, Problem 1

August 3, 2007
modular arithmeticfunctionnumber theory proposednumber theory

Problem Statement

Let p≥3 p \geq 3 be a prime, and let p p points A0,…,Ap−1 A_{0}, \ldots, A_{p-1} lie on a circle in that order. Above the point A1+⋯+k−1 A_{1+\cdots+k-1} we write the number k k for k=1,…,p k=1, \ldots, p (so 1 1 is written above A0 A_{0}). How many points have at least one number written above them?
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