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Four variable Diophantine equation with many squares

Source: Canada Repêchage 2021/6 CMOQR

March 30, 2021
CanadarepechageDiophantine equationalgebra

Problem Statement

Show that (w,x,y,z)=(0,0,0,0)(w, x, y, z)=(0,0,0,0) is the only integer solution to the equation w2+11x2−8y2−12yz−10z2=0w^{2}+11 x^{2}-8 y^{2}-12 y z-10 z^{2}=0
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