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x_0 is divisible by any prime factor of x

Source: China TST 2003

June 29, 2006
functionnumber theory unsolvednumber theory

Problem Statement

Let x0+2003y0x_0+\sqrt{2003}y_0 be the minimum positive integer root of Pell function x2−2003y2=1x^2-2003y^2=1. Find all the positive integer solutions (x,y)(x,y) of the equation, such that x0x_0 is divisible by any prime factor of xx.
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