Given that
find the value of
Find the sum of all solutions to the equation
A polynomial satisfies the equation . Find .
Let be a quintic polynomial such that
Determine .
Note: Many people are answering this incorrectly because they think it is the Fibonacci sequence, but this problem is asking about a quintic polynomial that passes through those points. That does not necessarily mean the next term behaves as the Fibonacci sequence would.
Given that are real numbers that satisfy the system of equations above, what is the sum of all distinct values of ?