Geodesic
Characterizing the sum of two cubes
Journal of integer sequences, Tome 6 (2003) no. 4
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.
Classification : 11A07, 11B13, 11B50, 11D25, 11D79, 11P05
Keywords: sum of two cubes, Diophantine equation (Concerned with sequence 
@article{JIS_2003__6_4_a4,
     author = {Broughan,  Kevin A.},
     title = {Characterizing the sum of two cubes},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {4},
     zbl = {1068.11022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a4/}
}
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Broughan,  Kevin A. Characterizing the sum of two cubes. Journal of integer sequences, Tome 6 (2003) no. 4. http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a4/