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Decomposition of an integer as a sum of two cubes to a fixed modulus. (English) Zbl 1299.11032

Summary: The representation of any integer as the sum of two cubes to a fixed modulus is always possible if and only if the modulus is not divisible by seven or nine. For a positive non-prime power there is given an inductive way to find its remainders that can be represented as the sum of two cubes to a fixed modulus \(N\). Moreover, it is possible to find the components of this representation.

MSC:

11D25 Cubic and quartic Diophantine equations
11A07 Congruences; primitive roots; residue systems
11D85 Representation problems
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