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\[\displaystyle \large H(x) = \sum_{p \, | \, x} \left(p*\log_p({\text{gcf}(x,p^{\lfloor \log_p x \rfloor})})\right)\] The idea for this function was adding together the largest ...

Let's use the Fundamental Theorem Algebra (FTA) and the Brahmagupta Fibonacci identity to prove that every non-negative polynnomial \(f(x) \in \mathbb{R}\left[ x \right]\) may be written ...

ABC is a random triangle. D, E and F are built by the given angles in the diagram.

Find the biggest angle in DEF.

Graph for reference

Like most of my notes, this one starts with curiosity. I saw this problem and went to Desmos to solve it. Then, I got a bit curious ...

An Archimedean solid has a vertex configuration \(\{n_1, n_2, ... , n_k\}\) if each vertex borders regular polygons with \(n_i\) number of sides, \(i=1,..., k\). For example, ...

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