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+ y + z + w = xy + yz + zx + w^2 - w = xyz - w^3 = - 1 diophantine

Source: 2011 Saudi Arabia Pre-TST November 3.4

January 1, 2022
number theorydiophantinesystem of equationsSystem

Problem Statement

Find all quadruples (x,y,z,w)(x,y,z,w) of integers satisfying the sys­tem of equations x+y+z+w=xy+yz+zx+w2−w=xyz−w3=−1x + y + z + w = xy + yz + zx + w^2 - w = xyz - w^3 = - 1
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