IMO Shortlist 2017 problem N7


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Dodao/la: arhiva
Oct. 3, 2019
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An ordered pair (x, y) of integers is a primitive point if the greatest common divisor of x and y is 1. Given a finite set S of primitive points, prove that there exist a positive integer n and integers a_0, a_1, \ldots , a_n such that, for each (x, y) in S, we have: a_0x^n + a_1x^{n-1} y + a_2x^{n-2}y^2 + \cdots + a_{n-1}xy^{n-1} + a_ny^n = 1.

Source: https://www.imo-official.org/problems/IMO2017SL.pdf