Solutions for a Class of the higherDiophantine equation

DOI

10.2991/icacsei.2013.3How to use a DOI?

Keywords

Higher Diophantine equation, integer solutions, integer ring, algebraic number theroy

Abstract

We studied the Diophantine equation x2+4n=y9. By using the elementary method and algebaic number theroy, we obtain the following concusions: (i) Let X be an odd number, one necessary condition which the equation has integer solutions is that 28n-1/3 contains some square factors. (ii) Let X be an even number, when n=9k(k 1), all integer solutions for the equation are(x, y)=(0,4k), when n=9k+4(k 0), all integer solutions are (x, y)=(29k+4, 22k+1), when n 1,2,3,5,6,7,8(mod9)the equation has no integer solution.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yin xia Ran
PY  - 2013/08
DA  - 2013/08
TI  - Solutions for a Class of the higherDiophantine equation
BT  - Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013)
PB  - Atlantis Press
SP  - 7
EP  - 9
SN  - 1951-6851
UR  - https://doi.org/10.2991/icacsei.2013.3
DO  - 10.2991/icacsei.2013.3
ID  - Ran2013/08
ER  -