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diophantine 3x3: a^3=abc+2a+2c, b^3=abc-c , c^3=abc-a+b

Source: 2016 Latvia BW TST P18

December 17, 2022
number theoryDiophantine Equationssystem of equations

Problem Statement

Solve the system of equations in integers: {a3=abc+2a+2cb3=abc−cc3=abc−a+b\begin{cases} a^3=abc+2a+2c \\ b^3=abc-c \\ c^3=abc-a+b \end{cases}
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