Tuesday, 21 January 2014

at least one pair of relatively prime numbers

Show that every set of n+1 positive integers, chosen from a set of 2n consecutive
integers, contains at least one pair of relatively prime numbers.

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