| Title:
|
On $X_1^4+4X_2^4=X_3^8+4X_4^8$ and $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$ (English) |
| Author:
|
Jena, Susil Kumar |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
23 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
113-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The two related Diophantine equations: $X_1^4+4X_2^4=X_3^8+4X_4^8$ and $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$, have infinitely many nontrivial, primitive integral solutions. We give two parametric solutions, one for each of these equations. (English) |
| Keyword:
|
Diophantine equation $A^4+nB^4=C^2$ |
| Keyword:
|
Diophantine equation $A^4-nB^4=C^2$ |
| Keyword:
|
Diophantine equation $X_1^4+4X_2^4=X_3^8+4X_4^8$ |
| Keyword:
|
Diophantine equation $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$ |
| MSC:
|
11D41 |
| MSC:
|
11D72 |
| idZBL:
|
Zbl 1350.11045 |
| idMR:
|
MR3436679 |
| . |
| Date available:
|
2016-01-19T13:46:51Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144800 |
| . |
| Reference:
|
[1] Choudhry, A.: The Diophantine equation $A^4 + 4B^4 = C^4+4D^4$.Indian J. Pure Appl. Math., 29, 1998, 1127-1128, Zbl 0923.11050, MR 1672759 |
| Reference:
|
[2] Dickson, L. E.: History of the Theory of Numbers.2, 1952, Chelsea Publishing Company, New York, |
| Reference:
|
[3] Guy, R. K.: Unsolved Problems in Number Theory.2004, Springer Science+Business Media Inc., New York, Third Edition. Zbl 1058.11001, MR 2076335 |
| Reference:
|
[4] Jena, S. K.: Beyond the Method of Infinite Descent.J. Comb. Inf. Syst. Sci., 35, 2010, 501-511, |
| . |
