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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.

Modular Arithmetic Operations Warmup

         

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

If you multiply a blue number by an orange number, what color will the product be?

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

If you add a blue number to a yellow number, what color will the sum be?

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

If you multiply a green number by a yellow number, what color will the product be?

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

What color is \(8 \times 17 \, ?\)

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

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