A Computer Motivated Study of Problems in Number Theory

Number Theory is a subject that fascinates both professional number-theorists and “recreational ” mathematicians. The reason is clear: the objects that are studied are concrete, thus useful intuitions about them can be developed through experimenting with easy examples. Moreover, employing the computer in such investigations enables many more cases to be verified than can be done manually, thus facilitating the statement of a true conjecture, which subsequently requires a proof. Additionally, it sometimes paves the way towards other, related conjectures. The aim of this paper is to report on such a scenario; namely, the presentation of a problem, its investigation using the computer and the subsequent problems which arose as a result. All of these explorations were interlaced with a study of the necessary number theoretic background to effectively tackle the evolving problems