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True or False?

\(\quad\) For all positive integers \(a\), \( \left \lfloor \dfrac{2^a}a \right \rfloor\) is even.

\( \lfloor \cdot \rfloor \) denotes the floor function.

This is a really hard functional equation by me:

Find all \(f: \mathbb{R} \rightarrow \mathbb{R}\) such that

\( f(x^2+f(y)^2)=xf(x)+yf(y) \) for ...

Given a triangle \(ABC\) with circumcenter \(O\), how many moves does it take to draw a line \(\ell\) through \(O\) where \(\ell\) intersects \(AB\) and \(AC\) at \(P\), \(Q\) such ...

Given two lines that meet at an angle of \(\alpha\), and a point \(P\), how many moves does it take to construct two points \(A,B\) such that ...

Given a circle (without the center) and a point \(P\) on the circle, how many moves does it take to draw a tangent to the circle at that point?

All ...

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