Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.6

Characterizing the Sum of Two Cubes


Kevin A. Broughan
University of Waikato
Hamilton 2001
New Zealand

Abstract: An intrinsic characterization of positive integers which can be represented as the sum or difference of two cubes is given. Every integer has a smallest multiple which is a sum of two cubes and such that the multiple, in the form of an iterated composite function of the integer, is eventually periodic with period one or two. 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 7 or 9.

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(Concerned with sequence A045980.)

Received March 31 2003; revised version received December 18 2003. Published in Journal of Integer Sequences January 14 2004.

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