#### 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

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.