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diophantine, a^3 -b^3 -c^3 = 3abc, a^2 = 2(a+b+c),

Source: 1984 Swedish Mathematical Competition p5

March 28, 2021
number theoryDiophantine equationsystem of equationsSystemdiophantine

Problem Statement

Solve in natural numbers a,b,ca,b,c the system {a3−b3−c3=3abca2=2(a+b+c)\left\{ \begin{array}{l}a^3 -b^3 -c^3 = 3abc \\ a^2 = 2(a+b+c)\\ \end{array} \right.
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