The aim of this project is to investigate the existence of Escher solutions. Specific questions that will be considered initially include:
(1) Is it true that the triples (2,2,r) (resp. (2,3,r)) have no Escher solution for all primes r ≥ 3 (resp. ≥ 7)?
(2) Is it true that for all prime p > 2, the triple (p, q, q) has no Escher solution for q a sufficiently large prime?
(3) Is the smallest element of a triple having no Escher solution always prime?
La Trobe University
Aidan Brohm is a student of La Trobe University studying a Bachelor of Science. He is majoring in Mathematics as it is a very keen interest of his. Aidan graduated in Bendigo from Catholic College in 2014. He loves sport and plays a lot of it himself, in particular Basketball. Aidan is in his 3rd year of studies with La Trobe however he is currently in his 2nd year of his course with aspirations to complete his masters and maybe one day a PhD, both in mathematics.