On integer solutions to x² - dy² = 1, z² - 2dy² =1

P. G. Walsh

Acta Arithmetica (1997)

  • Volume: 82, Issue: 1, page 69-76
  • ISSN: 0065-1036

How to cite

top

P. G. Walsh. "On integer solutions to x² - dy² = 1, z² - 2dy² =1." Acta Arithmetica 82.1 (1997): 69-76. <http://eudml.org/doc/207079>.

@article{P1997,
author = {P. G. Walsh},
journal = {Acta Arithmetica},
keywords = {quadratic diophantine equations; elliptic curves; fundamental units; quadratic fields; abc conjecture; simultaneous Pell equations},
language = {eng},
number = {1},
pages = {69-76},
title = {On integer solutions to x² - dy² = 1, z² - 2dy² =1},
url = {http://eudml.org/doc/207079},
volume = {82},
year = {1997},
}

TY - JOUR
AU - P. G. Walsh
TI - On integer solutions to x² - dy² = 1, z² - 2dy² =1
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 1
SP - 69
EP - 76
LA - eng
KW - quadratic diophantine equations; elliptic curves; fundamental units; quadratic fields; abc conjecture; simultaneous Pell equations
UR - http://eudml.org/doc/207079
ER -

References

top
  1. [1] M. A. Bennett, On the number of solutions to simultaneous Pell equations, J. Reine Angew. Math., to appear. Zbl1044.11011
  2. [2] J. H. E. Cohn, Eight Diophantine equations, Proc. London Math. Soc. (3) 16 (1966), 153-166. Zbl0136.02806
  3. [3] J. H. E. Cohn, Five Diophantine equations, Math. Scand. 21 (1967), 61-70. Zbl0169.37401
  4. [4] J. H. E. Cohn, The Diophantine equation x⁴-Dy²=1, II, Acta Arith. 78 (1997), 401-403. Zbl0870.11018
  5. [5] W. Ljunggren, Zur Theorie der Gleichung x²+1=Dy⁴, Avh. Norske Vid. Akad. Oslo (1942), 1-27. 
  6. [6] D. W. Masser, Open Problems, in: Proc. Sympos. Analytic Number Theory, W. W. L. Chen (ed.), London Imperial College, 1985. 
  7. [7] K. Ono, Euler's concordant forms, Acta Arith. 78 (1996), 101-123. 
  8. [8] N. Robbins, On Pell numbers of the form px², where p is a prime, Fibonacci Quart. (4) 22 (1984), 340-348. 
  9. [9] P. Samuel, Algebraic Theory of Numbers, Houghton Mifflin, Boston, 1970. 
  10. [10] W. Sierpiński, Elementary Theory of Numbers, Państwowe Wydawnictwo Naukowe, Warszawa, 1964. Zbl0122.04402
  11. [11] C. L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers III, J. London Math. Soc. (2) 28 (1983), 211-217. Zbl0491.10010

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.