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Process of adding rational numbers

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

April 19, 2023
combinatoricsnumber theory

Problem Statement

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)/(1āˆ’xy)(x+y)/(1-xy) to it. Prove that there is a rational number that cannot ever appear on the board.
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