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The numbers \(x_1, x_2, x_3, ..., x_{100}\) satisfy that \[\sum_{1\leq i < j\leq 100}{(ix_j-jx_i)^2}=338350\] and \[\sum_{i=1}^{100} {x_i}^2=1.\] Find ...

For all \(20\)-tuples of real numbers \((x_1, x_2, ..., x_{20}),\) find the maximum value of the number \(x_1\) such that ...

Find the maximum value of \(z\) for all the triples of real numbers \((x, y, z)\) that maximize \( (3y-2z)^2 + (z-3x)^2 + (2x-y)^2 \) on the unit sphere ...

My brother Jose gets paid his salary from work every other Friday, but he also receives a bonus of $1000 every time the payment day is one of the first ...

\[\large{2^{126}\prod_{k=1}^{126} \sin{\left(\theta +\frac{k\pi}{127}\right)}}\] The previous product of sines can be expressed in the form ...

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