Sunday, 13 October 2013

relatively prime

Two integers m and n are called relatively prime if (m,n) = 1. Prove that among any five consecutive positive integers there is one integer which is relatively prime to the other four integers.  
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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, ...