The Sum of Two Integer Cubes - Restricted

Abstract: We study the size of sets containing sums of two integer cubes such that their representation is unique and also fit between two consecutive integer cubes. We will try to write algorithms that efficiently calculate the size of these sets and also implement these algorithms in PythonTM. Although we will fail to find a non-iterative algorithm, we will find different ways of approximating the size of these sets. We will also find that techniques used in our failed algorithms can be used to calculate the number of integer lattice points inside a circle.