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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.

March 1, 2016 is Tuesday. What day of the week is April 1, 2016?

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6515 leaves a remainder of 4 upon division by 17.

3897 also leaves a remainder of 4 upon division by 17.

Then what is the remainder of 2618 upon division by 17?

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What is equivalent to \( 703 - 564 \pmod{7} \)?

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What is \(\underbrace{7+7+7+\ldots+7}_{\text{100 7's}}\ \bmod{6}?\)

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What is \( (83 + 23) \bmod{4} \)?

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