Representations of Numbers as Sums and Differences of Unlike Powers
Bollettino dell'Unione Matematica Italiana (2010)
- Volume: 3, Issue: 1, page 169-177
- ISSN: 0392-4041
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topJabara, Enrico. "Representations of Numbers as Sums and Differences of Unlike Powers." Bollettino dell'Unione Matematica Italiana 3.1 (2010): 169-177. <http://eudml.org/doc/290668>.
@article{Jabara2010,
abstract = {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.},
author = {Jabara, Enrico},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {169-177},
publisher = {Unione Matematica Italiana},
title = {Representations of Numbers as Sums and Differences of Unlike Powers},
url = {http://eudml.org/doc/290668},
volume = {3},
year = {2010},
}
TY - JOUR
AU - Jabara, Enrico
TI - Representations of Numbers as Sums and Differences of Unlike Powers
JO - Bollettino dell'Unione Matematica Italiana
DA - 2010/2//
PB - Unione Matematica Italiana
VL - 3
IS - 1
SP - 169
EP - 177
AB - 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.
LA - eng
UR - http://eudml.org/doc/290668
ER -
References
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