Bro , do you even Euler?

Number Theory Level 4

a3−b3−c3=3abca2=2(b+c) \begin{aligned} a^3-b^3-c^3&=&3abc \\ a^2 &=& 2(b+c) \\ \end{aligned}

Find the triplets (a,b,c)∈Z+(a,b,c) \in \mathbb {Z^{+}} that satisfy the system of equations above.

Details and assumptions:

  • Input the sum of all possible numbers in the triplets as an answer. As an explicit example, if (1,2,3)(1,2,3) is the only triplet, input 6 but if (2,3,4)(2,3,4) is also an answer input 15.
Arian Tashakkor by Arian Tashakkor
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