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diophantine system xy +zw = a, xz + yw = b has finitely solutions x,y,z,w

Source: IMAR 2009 p1

September 27, 2018
Diophantine equationalgebranumber theorysystem of equations

Problem Statement

Given aa and bb distinct positive integers, show that the system of equations xy+zw=ax y +zw = a xz+yw=bxz + yw = b has only finitely many solutions in integers x,y,z,wx, y, z,w.
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