Geodesic
Representations of Numbers as Sums and Differences of Unlike Powers
Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 169-177

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we prove that every $n \in \mathbf{Z}$ can be written as $$n=\epsilon_{1}x^{2}_{1} + \epsilon_{2}x^{3}_{2} + \epsilon_{3}x^{4}_{3} + \epsilon_{4}x^{5}_{4}$$ and as $$n=\epsilon_{1}x^{3}_{1} + \epsilon_{2}x^{4}_{2} + \epsilon_{3}x^{5}_{3} + \epsilon_{4}x^{6}_{4} + \epsilon_{5}x^{7}_{5} + \epsilon_{6}x^{8}_{6} + \epsilon_{7}x^{9}_{7} + \epsilon_{8}x^{10}_{8}$$ with $x_{i} \in \mathbf{Z}$ and $\epsilon_{i} \in \{-1,1\}$. We also prove some other results on numbers expressible as sums or differences of unlike powers. 
@article{BUMI_2010_9_3_1_a7,
     author = {Jabara, Enrico},
     title = {Representations of {Numbers} as {Sums} and {Differences} of {Unlike} {Powers}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {169--177},
     publisher = {mathdoc},
     volume = {Ser. 9, 3},
     number = {1},
     year = {2010},
     zbl = {1198.11037},
     mrnumber = {2605918},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a7/}
}
TY  - JOUR
AU  - Jabara, Enrico
TI  - Representations of Numbers as Sums and Differences of Unlike Powers
JO  - Bollettino della Unione matematica italiana
PY  - 2010
SP  - 169
EP  - 177
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a7/
LA  - en
ID  - BUMI_2010_9_3_1_a7
ER  - 
%0 Journal Article
%A Jabara, Enrico
%T Representations of Numbers as Sums and Differences of Unlike Powers
%J Bollettino della Unione matematica italiana
%D 2010
%P 169-177
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a7/
%G en
%F BUMI_2010_9_3_1_a7
Jabara, Enrico. Representations of Numbers as Sums and Differences of Unlike Powers. Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 169-177. http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a7/