On the number of solutions of the generalized Ramanujan-Nagell equation x ² - D = 2 n + 2

Maohua Le

Acta Arithmetica (1991)

  • Volume: 60, Issue: 2, page 149-167
  • ISSN: 0065-1036

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Maohua Le. "On the number of solutions of the generalized Ramanujan-Nagell equation $x²-D = 2^{n+2}$." Acta Arithmetica 60.2 (1991): 149-167. <http://eudml.org/doc/206430>.

@article{MaohuaLe1991,
author = {Maohua Le},
journal = {Acta Arithmetica},
keywords = {number of solutions; Ramanujan-Nagell equation},
language = {eng},
number = {2},
pages = {149-167},
title = {On the number of solutions of the generalized Ramanujan-Nagell equation $x²-D = 2^\{n+2\}$},
url = {http://eudml.org/doc/206430},
volume = {60},
year = {1991},
}

TY - JOUR
AU - Maohua Le
TI - On the number of solutions of the generalized Ramanujan-Nagell equation $x²-D = 2^{n+2}$
JO - Acta Arithmetica
PY - 1991
VL - 60
IS - 2
SP - 149
EP - 167
LA - eng
KW - number of solutions; Ramanujan-Nagell equation
UR - http://eudml.org/doc/206430
ER -

References

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  1. [1] F. Beukers, On the generalized Ramanujan-Nagell equation I, Acta Arith. 38 (1981), 389-410. Zbl0371.10014
  2. [2] P. G. L. Dirichlet, Sur une propriété des formes quadratiques à déterminant positif, J. Math. Pures Appl. (2) 1 (1856), 76-79. 
  3. [3] L.-K. Hua, Introduction to Number Theory, Springer, Berlin 1982. 
  4. [4] M.-H. Le, The diophantine equation x ² = 4 q n + 4 q m + 1 , Proc. Amer. Math. Soc. 106 (1989), 599-604. 
  5. [5] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, Mass., 1983. 
  6. [6] O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Leipzig 1929. Zbl55.0262.09
  7. [7] K. Petr, Sur l'équation de Pell, Časopis Pest. Mat. Fys. 56 (1927), 57- 66 (in Czech). 
  8. [8] N. Tzanakisand J. Wolfskill, The diophantine equation x ² = 4 q a / 2 + 4 q + 1 , with an application to coding theory, J. Number Theory 26 (1987), 96-116. Zbl0612.10013

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