Zottor, Faith Shadow2024-01-292024-01-292024https://hdl.handle.net/10539/37458A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2023This work primarily characterises the values of d in Pell equation X 2 −dY 2 = ±1 that have at least some specified number of the sequence of X or Y solutions belonging to some interesting sequence of positive integers.enThesis