Achievements
Posted: Wednesday, July 10, 2024James D. Shaw, Associate Professor Emeritus; and James Guyker, Professor Emeritus, Mathematics
James D. Shaw, associate professor emeritus of mathematics, and James Guyker, professor emeritus of mathematics, published a joint paper, “On Parametric and Matrix Solutions to the Diophantine Equation x2 + dy2 − z2 = 0 Where d Is a Positive Square-Free Integer,” in the International Journal of Mathematics and Mathematical Sciences (September 2023).
From the Abstract:
The well-known matrix-generated tree structure for Pythagorean triplets (i.e., when d = 1) is extended to the solutions of the above equation. The proof is based on a parametrization of these solutions as well as on a dual version of Fermat’s method of descent.
