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

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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. 
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/
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     title = {Representations of {Numbers} as {Sums} and {Differences} of {Unlike} {Powers}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {169--177},
     year = {2010},
     volume = {Ser. 9, 3},
     number = {1},
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     mrnumber = {2605918},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a7/}
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