Isn't 100000 such a huge number (Part-8)?

Algebra Level 5

\[\color{Purple}{a^{2}(a^{99998}+1)+b^{2}(b^{99998}+1)+c^{2}(c^{99998}+1)=2(a^{50000}b+b^{50000}c+c^{50000}a})\]

How many ordered triples \(\color{green}{(a,b,c)}\) are there where \(a,b\) and \(c\) are complex numbers and \(a^{50000}-b,b^{50000}-c\) and \(c^{50000}-a\) are rational numbers satisfying the equation above?

The answer can be expressed in the form \(x\times 10^{10}\).

Find the value of \(x\).

This problem is original.
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