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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