| Title:
|
Complete solution of a family of simultaneous Pellian equations (English) |
| Author:
|
Dujella, Andrej |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
6 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
59-67 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11D09 |
| MSC:
|
11D25 |
| idZBL:
|
Zbl 1024.11014 |
| idMR:
|
MR1822516 |
| . |
| Date available:
|
2009-01-30T09:06:02Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120541 |
| . |
| Reference:
|
[1] Baker A.: The diophantine equation $y^2 = ax^3 + bx^2 + cx + d$.J. London Math. Soc 43 (1968), 1-9. Zbl 0157.09801, MR 0231783, 10.1112/jlms/s1-43.1.1 |
| Reference:
|
[2] Baker A., Davenport H.: The equations $3x^2 - 2 = y^2$ and $8x^2 - 7 = z^2$.Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137. MR 0248079, 10.1093/qmath/20.1.129 |
| Reference:
|
[3] Bennett M.A.: On the number of solutions of simultaneous Pell equations.J. Reine Angew. Math., to appear. Zbl 1165.11034, MR 1629862 |
| Reference:
|
[4] Brown E.: Sets in which xy + k is always a square.Math. Comp. 45 (1985), 613-620. Zbl 0577.10015, MR 0804949 |
| Reference:
|
[5] Cohn J. H. E.: Lucas and Fibonacci numbers and some Diophantine equations.Proc. Glasgow Math. Assoc. 7 (1965), 24-28. Zbl 0127.01902, MR 0177944 |
| Reference:
|
[6] Dickson L. E.: History of the Theory of Numbers, Vol. 2.Chelsea, New York, 1966, pp. 518-519. |
| Reference:
|
[7] Diophantus of Alexandria: Arithmetics and the Book of Polygonal Numbers.(I.G. Bashmakova, Ed.), Nauka, Moscow, 1974 (in Russian), pp. 103-104, 232. |
| Reference:
|
[8] Dujella A.: Generalization of a problem of Diophantus.Acta Arith. 65 (1993), 15-27. Zbl 0849.11018, MR 1239240 |
| Reference:
|
[9] Dujella A.: The problem of the extension of a parametric family of Diophantine triples.Publ. Math. Debrecen 51 (1997), 311-322. Zbl 0903.11010, MR 1485226 |
| Reference:
|
[10] Dujella A.: A proof of the Hoggatt-Bergum conjecture.Proc. Amer. Math. Soc., to appear. Zbl 0937.11011, MR 1605956 |
| Reference:
|
[11] Dujella A.: An extension of an old problem of Diophantus and Euler.(preprint). Zbl 1125.11308, MR 1730070 |
| Reference:
|
[12] Dujella A., Petho A.: Generalization of a theorem of Baker and Davenport.Quart. J. Math. Oxford Ser. (2), to appear. |
| Reference:
|
[13] Gupta H. K., Singh K.: On k-triad sequences.Internat. J. Math. Math. Sci. 5 (1985), 799-804. Zbl 0585.10006, MR 0821637, 10.1155/S0161171285000886 |
| Reference:
|
[14] Kedlaya K. S.: Solving constrained Pell equations.Math. Comp., to appear. Zbl 0945.11027, MR 1443123 |
| Reference:
|
[15] Mohanty S. P., Ramasamy A. M. S.: The simultaneous Diophantine equations $5y^2 - 20 = x^2$ and $2y^2 + 1 = z^2$.J. Number Theory 18 (1984), 356-359. MR 0746870, 10.1016/0022-314X(84)90068-4 |
| Reference:
|
[16] Mohanty S. P., Ramasamy A.M.S.: On $P_{r,k}$ sequences.Fibonacci Quart. 23 (1985), 36-44. MR 0786359 |
| Reference:
|
[17] Nagell T.: Introduction to Number Theory.Almqvist, Stockholm, Wiley, New York, 1951. Zbl 0042.26702, MR 0043111 |
| Reference:
|
[18] Rickert J. H.: Simultaneous rational approximations and related diophantine equations.Math. Proc. Cambridge Philos. Soc. 113 (1993), 461-472. Zbl 0786.11040, MR 1207511, 10.1017/S0305004100076118 |
| Reference:
|
[19]
: SIMATH Manual.Universität des Saarlandes, Saarbrücken, 1993. |
| . |
