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Prove that there are infinte...

Source: INMO 2001 Problem 2

October 10, 2005
modular arithmeticalgebrapolynomialarithmetic sequencenumber theory solvednumber theory

Problem Statement

Show that the equation x2+y2+z2=(x−y)(y−z)(z−x)x^2 + y^2 + z^2 = ( x-y)(y-z)(z-x) has infintely many solutions in integers x,y,zx,y,z.
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