Date of Graduation

5-2026

Document Type

Thesis

Degree Name

Bachelor of Science in Mathematics

Degree Level

Undergraduate

Department

Mathematical Sciences

Advisor/Mentor

John Bergdall

Committee Member

Ariel Barton

Second Committee Member

Matthew Day

Third Committee Member

Paolo Mantero

Abstract

Primitive Pythagorean triples (PPTs) are (a,b,c) triples that satisfy the Pythagorean theorem and share no other common factors outside of 1. This project examines these PPTs reduction modulo odd prime powers by combining proof writing and number-theoretical analysis with the process of verification and formalization in the Lean proof coding language. Using the parameterization of PPTs generated by using the unit circle with additional conditions, we investigate how these triples behave modulo  for odd primes , with emphasis on counting the number of elements in the set of PPTs (a,b,c) modulo pn . By using cases based on initial conditions (e.g., whether parameters are nonzero mod p), we derive congruence relations that determine when two parameterizations yield equivalent reductions and how properties of PPTs still are satisfied modulo pn. These mathematical arguments and results are fully or partially formalized in Lean, attempting to translating classical mathematical arguments into Lean code. This part emphasis the precision and effort required for the formalization of mathematical proofs and demonstrates the current difficulties of working with an evolving computer coding language and proof assistant Lean. This project demonstrates how the process of mathematical formalization proceeds, while also illustrating the interaction between abstract mathematical reasoning and its implementation in a theorem-proving computer environment such as Lean.

Keywords

Number Theory; Lean

Download

Share

COinS