# Degree 99 Polynomial

Algebra Level 5

$$f(x)$$ is a polynomial of degree 99. For exactly 100 (out of 101) integer values ranging from $$0$$ to $$100$$, we have $$f(x) = \frac {1}{x+1}$$. Also, $$f(101) = 0$$. For what value of $$a$$, $$0 \leq a \leq 100$$ is $$f(a) \neq \frac {1}{a+1}$$?

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