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# Number Theory Warmups

If numbers aren't beautiful, we don't know what is. Dive into this fun collection to play with numbers like never before, and start unlocking the connections that are the foundation of Number Theory.

Which one is the golden goblet?

\[\Huge {\color{blue}9}^{{\color{green}8}^{{\color{red}7}^{{\color{brown}6} ^{\color{magenta}5}}}}\]

What are the last two digits when this integer fully expanded out?

There is a prime number \(p\) such that \(16p+1\) is the cube of a positive integer. Find \(p\).

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