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factorization and x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2=2000 in ZxZxZ

Source: Greece JBMO TST 2001 p1

June 17, 2019
number theoryalgebrafactorizationDiophantine equation

Problem Statement

a) Factorize A=x4+y4+z4−2x2y2−2y2z2−2z2x2A= x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2 b) Prove that there are no integers x,y,zx,y,z such that x4+y4+z4−2x2y2−2y2z2−2z2x2=2000x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2=2000
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