# An equation involving 2760.

Number Theory Level 5

Find the number of ordered triples of integers $$(a,b,c)$$ that satisfy the equation $a(b-c)^3+b(c-a)^3+c(a-b)^3=2760.$

Note that the order matters: $$(-8,-5,15)$$ and $$(15,-8,-5)$$ are considered different solutions.

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