1987 USAMO Problems/Problem 3

Problem

$X$ is the smallest set of polynomials $p(x)$ such that:

1. $p(x) = x$ belongs to $X$ .

2. If $r(x)$ belongs to $X$ , then $x\cdot r(x)$ and $(x + (1 - x) \cdot r(x) )$ both belong to $X$ .

Show that if $r(x)$ and $s(x)$ are distinct elements of $X$ , then $r(x) \neq s(x)$ for any $0 < x < 1$ .

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1987 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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