Let a, b, c, d be integers.
Show that the product (a - b)(a - c)(a - d)(b - c)(b - d)(c - d) is divisible by 12.
Show that the product (a - b)(a - c)(a - d)(b - c)(b - d)(c - d) is divisible by 12.
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...
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