Saturday 28 September 2013

Natural Numbers

Find all natural numbers n such that the number n(n + 1)(n + 2)(n + 3) has exactly three di fferent prime  divisors.

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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...