Algebra
# Systems of Equations

What is $a^4 + b^4 + c^4$?

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).