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# Euler's Theorem

Euler's theorem relate to the remainder of various powers and has applications ranging from modern cryptography to recreational problem-solving.

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How many positive integers \(n>1\) evenly divide \(a^{13}-a\) for all positive integers \(a?\)

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Paola Ramírez**

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Michał Jesionowski**

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

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

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Kalpok Guha**

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Dylan Pentland**

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Find the tens digit of \[ \Large 2014^{2014^{2014}}. \]

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Steven Yuan**

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