13

Part of 2006 China Second Round Olympiad

Problems(1)

2006 China Second Round Olympiad Test 1 #13

Source:

Given an integer

n\ge 2

M_0 (x_0, y_0)

to be an intersection point of the parabola

y^2=nx-1

y=x

. Prove that for any positive integer

m

, there exists an integer

k\ge 2

(x^m_0, y^m_0)

is an intersection point of

y^2=mx-1

y=x