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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.

# Addition and Subtraction

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

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?

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

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

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

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