## Achievements

Posted: Wednesday, July 10, 2024### James 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 *x*^{2} + d*y*^{2} − *z*^{2} = 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.