# Polynomial Reciprocal on Integers

Algebra Level 3

$$f(x)$$ is a degree 4 polynomial satisfying $$f(n) = \frac {1} {n}$$ for integers $$n =$$ 1 to 5. If $$f(0) = \frac {a} {b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

×