Decomposition of an integer as a sum of two cubes to a fixed modulus

Abstract

The representation of any integer as the sum of two cubes to a fixedmodulus is always possible if and only if the modulus is not divisibleby seven or nine. For a positive non-prime power there is given aninductive way to find its remainders that can be represented as the sumof two cubes to a fixed modulus $N$. Moreover, it is possible to findthe components of this representation.