Sunday 10 November 2013

((n!)!)!

Find the largest number n such that (2004!)! is divisible by ((n!)!)!
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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, &a...