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Bounding Diophantine Equation

Source: China Additional TST for IMO 2020, P4

October 20, 2020
number theoryDiophantine equation

Problem Statement

Show that the following equation has finitely many solutions (t,A,x,y,z)(t,A,x,y,z) in positive integers t(1−A−2)(1−x−2)(1−y−2)(1−z−2)=(1+x−1)(1+y−1)(1+z−1)\sqrt{t(1-A^{-2})(1-x^{-2})(1-y^{-2})(1-z^{-2})}=(1+x^{-1})(1+y^{-1})(1+z^{-1})
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