On X 1 4 + 4 X 2 4 = X 3 8 + 4 X 4 8 and Y 1 4 = Y 2 4 + Y 3 4 + 4 Y 4 4

Susil Kumar Jena

Communications in Mathematics (2015)

  • Volume: 23, Issue: 2, page 113-117
  • ISSN: 1804-1388

Abstract

top
The two related Diophantine equations: X 1 4 + 4 X 2 4 = X 3 8 + 4 X 4 8 and Y 1 4 = Y 2 4 + Y 3 4 + 4 Y 4 4 , have infinitely many nontrivial, primitive integral solutions. We give two parametric solutions, one for each of these equations.

How to cite

top

Jena, Susil Kumar. "On $X_1^4+4X_2^4=X_3^8+4X_4^8$ and $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$." Communications in Mathematics 23.2 (2015): 113-117. <http://eudml.org/doc/276029>.

@article{Jena2015,
abstract = {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.},
author = {Jena, Susil Kumar},
journal = {Communications in Mathematics},
keywords = {Diophantine equation $A^4+nB^4=C^2$; Diophantine equation $A^4-nB^4=C^2$; Diophantine equation $X_1^4+4X_2^4=X_3^8+4X_4^8$; Diophantine equation $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$},
language = {eng},
number = {2},
pages = {113-117},
publisher = {University of Ostrava},
title = {On $X_1^4+4X_2^4=X_3^8+4X_4^8$ and $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$},
url = {http://eudml.org/doc/276029},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Jena, Susil Kumar
TI - On $X_1^4+4X_2^4=X_3^8+4X_4^8$ and $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$
JO - Communications in Mathematics
PY - 2015
PB - University of Ostrava
VL - 23
IS - 2
SP - 113
EP - 117
AB - 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.
LA - eng
KW - Diophantine equation $A^4+nB^4=C^2$; Diophantine equation $A^4-nB^4=C^2$; Diophantine equation $X_1^4+4X_2^4=X_3^8+4X_4^8$; Diophantine equation $Y_1^4=Y_2^4+Y_3^4+4Y_4^4$
UR - http://eudml.org/doc/276029
ER -

References

top
  1. Choudhry, A., The Diophantine equation A 4 + 4 B 4 = C 4 + 4 D 4 , Indian J. Pure Appl. Math., 29, 1998, 1127-1128, (1998) Zbl0923.11050MR1672759
  2. Dickson, L. E., History of the Theory of Numbers, 2, 1952, Chelsea Publishing Company, New York, (1952) 
  3. Guy, R. K., Unsolved Problems in Number Theory, 2004, Springer Science+Business Media Inc., New York, Third Edition. (2004) Zbl1058.11001MR2076335
  4. Jena, S. K., Beyond the Method of Infinite Descent, J. Comb. Inf. Syst. Sci., 35, 2010, 501-511, (2010) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.