Solutions for a Class of the higherDiophantine equation
Yin xia Ran
Yin xia Ran
Available Online August 2013.
- 10.2991/icacsei.2013.3How to use a DOI?
- Higher Diophantine equation, integer solutions, integer ring, algebraic number theroy
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.
- © 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/).
Cite this article
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 -