Abstract Title
The Brahmagupta Triples and Record Numbers
Additional Funding Sources
The research described was supported by Boise State University.
Abstract
In the spring 2020 semester, one group assignment in the course Communication in the Mathematical Sciences at Boise State University, taught by Dr. Marion Scheepers, instructed students to write a paper which explores Brahmagupta N-triples. A triple (x,y,k) of integers is a Brahmagupta N-triple if the equation x2-Ny2=k holds for them. Two groups found a previously unknown sequence of Brahmagupta N-triples involving record primes. This finding led to new research questions and the current project. This project investigates whether there are for each k patterns related to the N, x, or y for new record values of x or y coefficients at corresponding N, relations among these record coefficients, possible growth patterns, and modular patterns for record N's, and whether for these record values the number N is required to be a prime number.
The Brahmagupta Triples and Record Numbers
In the spring 2020 semester, one group assignment in the course Communication in the Mathematical Sciences at Boise State University, taught by Dr. Marion Scheepers, instructed students to write a paper which explores Brahmagupta N-triples. A triple (x,y,k) of integers is a Brahmagupta N-triple if the equation x2-Ny2=k holds for them. Two groups found a previously unknown sequence of Brahmagupta N-triples involving record primes. This finding led to new research questions and the current project. This project investigates whether there are for each k patterns related to the N, x, or y for new record values of x or y coefficients at corresponding N, relations among these record coefficients, possible growth patterns, and modular patterns for record N's, and whether for these record values the number N is required to be a prime number.