Jabara, Enrico:
Representations of Numbers as Sums and Differences of Unlike Powers
Bollettino dell'Unione Matematica Italiana Serie 9 3 (2010), fasc. n.1, p. 169-177, (English)
pdf (288 Kb), djvu (86 Kb). | MR 2605918 | Zbl 1198.11037
Sunto
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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Con il contributo del Ministero per i Beni e le Attività Culturali