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Vieta root jumping is a descent method that occurs when you have to solve a Diophantine equation whose solutions have a recursive structure. Popular in advanced math olympiad number theory problems.

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What is \(a^4 + b^4 + c^4\)?

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An ordered triple of real numbers \( (a, b, c) \) is called friendly, if each number is equal to the product of the other 2. How many (distinct) friendly triples are there?

**Details and assumptions**

The numbers need not be pairwise distinct (which means that no two of them are the same).

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