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Characterizing the Sum of Two Cubes
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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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