olymmath

USAMO 1975 Problem 3

  • Day 1
  • Answer

A polynomial p(x)p(x) of degree nn satisfies p(0)=0,p(1)=1/2,p(2)=2/3,…,p(n)=n/(n+1)p(0)=0, p(1)=1 / 2, p(2)=2 / 3, \ldots, p(n)=n /(n+1). Find p(n+1)p(n+1).

Dataset text NuminaMath olympiads. Quoted with source.

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p(n+1)=\begin{cases} 1, & \text{if } n \text{ is odd} \ \frac{n}{n+2}, & \text{if } n \text{ is even} \end{cases}

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