The Intricacies of Pairwise Modular Multiplicative Inverse in Lucas Numbers

Authors

Charles Liu, Pullman High SchoolFollow

Abstract

Let (p,q) be a pair of relatively prime integers greater than 1. The pairwise modular multiplicative inverse (PMMI) of (p,q) is defined as the unique pair of positive integers (p′, q′) such that p p′ ≡ 1 (mod q), p′ < q, qq′ ≡ 1 (mod p), q′ < p. In this paper, we determine all pairs of Lucas numbers such that their PMMIs are pairs of Lucas numbers.

Author Bio

Charles Liu is a junior at the Pullman High School and running start student at the Washington State University (enrolled in WSU classes). He has a passion in mathematics and computer science and has participated in many competitions alongside the Pullman High School Math Team.

His interests and curiosities lie in number theory and software development. He hopes to continue his education at the collegiate level and continue to pursue his interests while expanding his horizons.

Faculty Sponsor

Professor Sheng-Chi Liu

Recommended Citation

Liu, Charles (2024) "The Intricacies of Pairwise Modular Multiplicative Inverse in Lucas Numbers," Rose-Hulman Undergraduate Mathematics Journal: Vol. 25: Iss. 2, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol25/iss2/9