Polynomial Reciprocal on Integers

Algebra Level 3

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

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