Thursday, 15 July 2021

Find the number of pairs (m,n) of positive integers with 1≤m<n≤30 such that there exists a real number x satisfying sin⁡(mx)+sin⁡(nx)=2.
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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, ...