Saturday, 26 October 2013

degree exactly 5

How many polynomials of degree exactly 5 with real coeffi cients send the set {1, 2, 3, 4, 5, 6} to a
permutation of itself?

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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...