Find those Triplets!

Algebra Level 5

Find the number of triples of integers a<b<ca<b<c with a≥−10a\geq -10, such that a(b−c)3+b(c−a)3+c(a−b)3=0.a(b-c)^3+b(c-a)^3+c(a-b)^3=0.

Calvin Lin by Calvin Lin
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