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
Primes, Divisibility, and Modular Arithmetic
Contributor(s): Joshua Zucker
Math Circles: MTC Network
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.
Activity Guide
This guide looks at the activity in detail and goes into the underlying math.
