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good years. when N-edition divides N(N+1)

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2022 p5

March 26, 2024
number theory

Problem Statement

The 11st edition of OLCOMA was organized in 19891989, so in 20222022 the 3434th edition will be celebrated. Suppose that the Olympics will continue to be held annually without interruption. We say that a year NN is good if the OLCOMA edition number of that year divides the product N(N+1)N(N +1). For example, the year 20222022 is good because 3434 divides 2022⋅20232022 \cdot 2023. Determine the last year NN in the 2121st century, 2000≤N≤20992000\le N \le 2099, which is good.
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