2014/11/13 by Bradford, Kyle, Ionascu, Eugen
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1411.3403
In this paper we will explore the solutions to the diophantine equation in the Erdős-Straus conjecture. For a prime p we are discussing the relationship between the values x,y,z ∈ ℕ so that (4)/(p) = (1)/(x) + (1)/(y) + (1)/(z). We will separate the types of solutions into two cases. In particular we will argue that the most common relationship found is x = \lfloor (py)/(4y-p) \rfloor + 1. Finally, we will make a few conjectures to motivate further research in this area.