# 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 $$x$$.

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