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# Introduction

If all integers are colored in the same pattern as the numbers in this grid, what color is 1234?

**Modular arithmetic** is the part of number theory used to study *cyclical* systems: systems where taking enough steps “forward” brings you back to where you started. In this quiz we'll focus exclusively on abstract coloring patterns so that we can find some general shortcuts for working with these systems.

In the modular arithmetic units later in this course, we'll expand these theories and more into shortcuts that can be applied to many real-life modular systems:

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

**Note:** Assume that *all* integers are colored according to the same pattern as the numbers in the grid.

**Note:** Assume that *all* integers are colored according to the same pattern (blue, then green, then orange) as the numbers in the grid.

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