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The remainder of 1+2+...+k

Source: Korea National Olympiad 2010 Problem 8

September 9, 2012
modular arithmeticnumber theory proposednumber theory

Problem Statement

There are 2010 2010 people sitting around a round table. First, we give one person x x a candy. Next, we give candies to 11 st person, 1+21+2 th person, 1+2+3 1+2+3 th person, ⋯\cdots , and 1+2+⋯+20091+2+\cdots + 2009 th person clockwise from x x . Find the number of people who get at least one candy.
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