Event Title

Identifying Patterns in Modular Arithmetic

Faculty Sponsor(s)

Emma Wright

Abstract

Is it ever true that 2+2 = 0? It is true under addition modulus 4. There are some very distinctive patterns in modular arithmetic, and we can visualize these patterns in modular multiplication tables. For example, we observe an inverse pattern in the columns of modular multiplication tables. Additionally, we prove a generalized formula for these patterns in any modulus. Ultimately, we identify many patterns that lead to much more complex and insightful formulas.

Location

Hartman Union Building Courtroom

Start Date

5-2-2019 2:00 PM

End Date

5-2-2019 3:00 PM

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May 2nd, 2:00 PM May 2nd, 3:00 PM

Identifying Patterns in Modular Arithmetic

Hartman Union Building Courtroom

Is it ever true that 2+2 = 0? It is true under addition modulus 4. There are some very distinctive patterns in modular arithmetic, and we can visualize these patterns in modular multiplication tables. For example, we observe an inverse pattern in the columns of modular multiplication tables. Additionally, we prove a generalized formula for these patterns in any modulus. Ultimately, we identify many patterns that lead to much more complex and insightful formulas.