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# Modular Arithmetic Operations

Considering the remainder "modulo" an integer is a powerful, foundational tool in Number Theory. You already use in clocks and work modulo 12.

What is the last digit when

\[ 1234 \times 5678 \]

is multiplied out?

If today is a Monday, then what day will it be 100 days later?

\[ \LARGE \color{red} 5^{\color{blue}8^{\color{green}{12}^{\color{purple}{15}^{\color{brown}{104}}}}} + \color{red}1\]

Determine the smallest prime divisor of the gigantic number above.

Which one is the golden goblet?

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