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

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What is \( 78 \times 49 \pmod{26} \)?

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What is \(\underbrace{\left(6\cdot 6 \cdot 6 \cdots 6\right)}_{\text{15 6's}} \ \bmod{7}?\)

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What is equivalent to

\[ 1!+2!+3!+ \cdots + 100! \pmod{12}? \]

Give your answer as an integer between 0 and 11, inclusive.

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What is \( (10 \times 85) \pmod{5} ?\)

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