MathDB

2

Part of 1992 IMO Longlists

Problems(1)

Prove that x,y exist

Source:

9/1/2010
Let mm be a positive integer and x0,y0x_0, y_0 integers such that x0,y0x_0, y_0 are relatively prime, y0y_0 divides x02+mx_0^2+m, and x0x_0 divides y02+my_0^2+m. Prove that there exist positive integers xx and yy such that xx and yy are relatively prime, yy divides x2+mx^2 + m, xx divides y2+my^2 + m, and x+y≤m+1.x + y \leq m+ 1.
number theoryrelatively primeDivisibilityIMO ShortlistIMO Longlist