MathDB

8

Part of 2022 239 Open Mathematical Olympiad

Problems(2)

Problem 8

Source: 239-School Open Olympiad (Senior Level)

4/25/2022
Prove that there is positive integers NN such that the equation arctan(N)=∑i=12020aiarctan(i),arctan(N)=\sum_{i=1}^{2020} a_i arctan(i), does not hold for any integers ai.a_{i}.
algebranumber theoryTrignometry
Process of adding rational numbers

Source: 239-School Open Olympiad 2022, Junior League P8

4/19/2023
There are several rational numbers written on a board. If the numbers xx{} and yy{} are present on the board, we can add the number (x+y)/(1−xy)(x+y)/(1-xy) to it. Prove that there is a rational number that cannot ever appear on the board.
combinatoricsnumber theory