MathDB
2006 China Second Round Olympiad Test 1 #13

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September 28, 2014
conicsparabola

Problem Statement

Given an integer n≥2n\ge 2, define M0(x0,y0)M_0 (x_0, y_0) to be an intersection point of the parabola y2=nx−1y^2=nx-1 and the line y=xy=x. Prove that for any positive integer mm, there exists an integer k≥2k\ge 2 such that (x0m,y0m)(x^m_0, y^m_0) is an intersection point of y2=mx−1y^2=mx-1 and the line y=xy=x.
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