Which pairs of rational numbers x and y satisfy the equation 3x^3 + 4y^3 = 5? It turns out there are none, but this is not easy to prove. Descent is a method going back to Fermat which can be used to attack such questions. Nowadays with the help of computer algebra packages we can apply descent techniques much more broadly. The aim of this project to develop and implement algorithms for carrying out descent on new classes of equations such as pairs of quadratic equations in 3 variables.
Supervisors
Supervisor: Brendan Creutz
Does the project come with funding
No
Final date for receiving applications
Ongoing
Keywords
Number theory, algebra, geometry
