Skip to content # Primes, Divisibility, and Modular Arithmetic

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

Zucker, Josh. (2020). Primes, Divisibility, and Modular Arithmetic. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/primes-divisibility-and-modular-arithmetic

Contributor(s): Joshua Zucker

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

Number theory is all about adding and multiplying integers: pretty simple stuff, good for elementary school or for PhD mathematicians. Dr. Arnold Ross says of number theory, that the purpose is “to think deeply of simple things.” So let’s do that together.
This session includes multiple problem sets beginning with prime numbers, continuing to divisibility and its rules, and concluding with Modulo (Modular Arithmetic).

MP1 - Make sense of problems and persevere in solving them.

MP2 - Reason abstractly and quantitatively.

MP3 - Construct viable arguments and critique others' reasoning.

MP4 - Model with mathematics.

MP5 - Use appropriate tools strategically.

MP6 - Attend to precision.

MP7 - Look for and make use of structure.

MP8 - Look for and express regularity in repeated reasoning.

MP2 - Reason abstractly and quantitatively.

MP3 - Construct viable arguments and critique others' reasoning.

MP4 - Model with mathematics.

MP5 - Use appropriate tools strategically.

MP6 - Attend to precision.

MP7 - Look for and make use of structure.

MP8 - Look for and express regularity in repeated reasoning.