In this project Sage will be used to explore open problems in Number Theory. The main problem that will be explored will be that of which integers d does the equation x squared minus d times y squared equal negative four have solutions in odd integers. This is related to open research problems, and obtaining more numerical data could help make progress in these areas.
The University of Newcastle
Cameron Shaw-Carmody is currently enrolled at the University of Newcastle in a double degree of Bachelor of Mathematics, majoring in Pure Mathematics/Bachelor of Science with a Physics major. He intends undertaking Honours in Mathematics after completing his double degree with a view to postgraduate study that will enable him to be an academic. His research interests are Number Theory, Algebra and Theoretical Physics. At present he is engaged in a project based on computer modelling in Matlab, and he will follow this with research on experimental Number Theory using the computer program Sage. Cameron hopes that his background in both Physics and Mathematics will inform his research in both.