Sulla risoluzione per numeri interi della equazione x 3 + y 3 + z 3 = u 3

Cataldo Agostinelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1975)

  • Volume: 59, Issue: 6, page 635-642
  • ISSN: 0392-7881

Abstract

top
In this paper the author considers the entire, positive or negative, solutions of the equation x 3 + y 3 + z 3 = u 3 , and establishes various formulas expressing the unknowns by means of two, three or four arbitrary parameters. The question has geometrical interest for the determination of the rational points of the cubic surface X 3 + Y 3 + Z 3 = 1 .

How to cite

top

Agostinelli, Cataldo. "Sulla risoluzione per numeri interi della equazione $x^{3} + y^{3} + z^{3} = u^{3}$." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 59.6 (1975): 635-642. <http://eudml.org/doc/290849>.

@article{Agostinelli1975,
author = {Agostinelli, Cataldo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {12},
number = {6},
pages = {635-642},
publisher = {Accademia Nazionale dei Lincei},
title = {Sulla risoluzione per numeri interi della equazione $x^\{3\} + y^\{3\} + z^\{3\} = u^\{3\}$},
url = {http://eudml.org/doc/290849},
volume = {59},
year = {1975},
}

TY - JOUR
AU - Agostinelli, Cataldo
TI - Sulla risoluzione per numeri interi della equazione $x^{3} + y^{3} + z^{3} = u^{3}$
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1975/12//
PB - Accademia Nazionale dei Lincei
VL - 59
IS - 6
SP - 635
EP - 642
LA - ita
UR - http://eudml.org/doc/290849
ER -

References

top
  1. SIERPINSKI, W. (1964) - Elementary theory of numbers, Chap. XI. Warszawa. MR47060
  2. EULER, - Opera omnia (1), I, 490-7. 
  3. DICKSON, L. E. (1920) - History of the theory of numbers, vol. II, Chap. XXI, p. 552. Washington. Zbl47.0888.08MR245501
  4. MORDELL, L. J. (1942) - On sums of three cubes, «J. London Math. Soc.», 17, 139-144. Zbl68.0067.03MR7761DOI10.1112/jlms/s1-17.3.139
  5. SEGRE, B. (1943) - A note on arithmetical properties of cubic surfaces, «J. London Math. Soc.», 18, 24-31; (1943) - On a parametric solution of the equation x 3 + y 3 + a ⁢ z 3 = b and on ternary forms representing every rational number, «J. London Math Soc.», 18, 31-34; (1944) - On arithmetical properties of singular cubic surface, «J. London Math. Soc.», 19, 24-91; (1949) - Sur les points entiers des surfaces cubiques. «Colloque Internat. d'Algèbre et theory on numbers», Paris81-82; - On the rational solutions of homogeneon. cubic equations in four variables, «Mathematical Notae», 11 (1-2); (1942) - The non singular cubic surfaces. Claredon Press. MR9471DOI10.1112/jlms/s1-18.1.24

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.