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Josh is flipping his phone as he waits for the subway. He finds that he can flip it stably around two of the three axes shown in the diagram. Curiously ...

\[x^2 + xy + y^2 = z^2\]

Let \(x,y,\) and \(z\) be prime numbers satisfying the equation above. What is the largest possible product \(xyz\)?

There is a biased coin whose probability of getting a head at the \(i^\text{th}\) flip in a game of 2017 flips be given by ...

\[\large \lim_{n\to\infty} \sqrt[n^2]{{n \choose1}{n \choose 2}\cdots{n \choose n}}\]

Find the closed form of the limit above to 3 decimal places.

Notation ...

\[ \large \int^{\infty }_{0}\frac{\cos ( \pi x) }{4x^{2}+1} \, dx=\dfrac1B{\pi e^{\frac{-\pi }{A} }} \]

The equation above holds true for some positive integers \(A\) and ...

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