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. 
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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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