#### Title (All Applicants)

The Last Digits of Infinity (On Tetrations Under Modular Rings)

#### Project Advisor(s) (Students Only)

Dr. Tom Bengtson

#### Presentation Type (All Applicants)

Oral Presentation

#### Disciplines (All Applicants)

Algebra | Number Theory

#### Description, Abstract, or Artist's Statement

A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there is convergent behavior. We will show that, in general, this convergent behavior will always show up.

#### Augustana Digital Commons Citation

Stowe, William. "The Last Digits of Infinity (On Tetrations Under Modular Rings)" (2019). *Celebration of Learning.*

https://digitalcommons.augustana.edu/celebrationoflearning/2019/presentations/9

The Last Digits of Infinity (On Tetrations Under Modular Rings)

A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there is convergent behavior. We will show that, in general, this convergent behavior will always show up.