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x + y +z = 2010, x^2 + y^2 + z^2 - xy - yz - zx =3

Source: 2010 Saudi Arabia Pre-TST 2.1

December 28, 2021

diophantinesystem of equationsSystemnumber theory

Problem Statement

Find all triples

(x,y,z)

of positive integers such that

\begin{cases} x + y +z = 2010 \\x^2 + y^2 + z^2 - xy - yz - zx =3 \end{cases}