| Title:
|
Pure powers and power classes in recurrence sequences (English) |
| Author:
|
Kiss, Péter |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
44 |
| Issue:
|
5 |
| Year:
|
1994 |
| Pages:
|
525-529 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11B37 |
| MSC:
|
11D61 |
| idZBL:
|
Zbl 0831.11019 |
| idMR:
|
MR1338426 |
| . |
| Date available:
|
2009-09-25T11:01:12Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136626 |
| . |
| Reference:
|
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| Reference:
|
[2] COHN J. H. E.: On souare Fibonacci numbers.J. London Math. Soc. 39 (1964), 537-540. MR 0163867 |
| Reference:
|
[3] COHN J. H. E.: Squares in some recurrent sequences.Pacific J. Math. 41 (1972), 631-646. Zbl 0248.10016, MR 0316367 |
| Reference:
|
[4] COHN J. H. E.: Eight Diophantine equations.Proc. London Math. Soc. 16 (1966), 153-166. Zbl 0136.02806, MR 0190078 |
| Reference:
|
[5] COHN J. H. E.: Five Diophatine equations.Math. Scand. 21 (1967), 61-70. MR 0236103 |
| Reference:
|
[6] KISS P.: Differences of the terms of linear recurrences.Studia Sci. Math. Hungar. 20 (1985), 285-293. Zbl 0628.10008, MR 0886031 |
| Reference:
|
[7] LJUNGGREN W.: Zur Theorie der Gleichung $x^2 + 1 = Dy$4.Avh. Norske Vid Akad. Oslo. 5 (1942). MR 0016375 |
| Reference:
|
[8] LONDON J.-FINKELSTEIN R.: On Fibonacci and Lucas numbers which are perfect powers.Fibonacci Quart. 7 (1969), 476-481, 487 (Errata ibid 8 (1970), 248). Zbl 0206.05402, MR 0255482 |
| Reference:
|
[9] LONDON J.-FINKELSTEIN R.: On Mordell's Equation $y^2 - k = x^3$.Bowling Green University Press, 1973. |
| Reference:
|
[10] McDANIEL W. L.-RIBENBOIM P.: Squares and double-squares in Lucas sequences.C.R. Math. Rep. Acad. Sci. Canada. 14 (1992), 104-108. Zbl 0771.11012, MR 1167065 |
| Reference:
|
[11] PETHO A.: Full cubes in the Fibonacci sequence.Publ. Math. Debrecen. 30 (1983), 117-127. MR 0733078 |
| Reference:
|
[12] PETHO A.: The Pell sequence contains only trivial perfect powers.In: Sets, Graphs and Numbers. Colloq. Math. Soc. Janos Bolyai 60, North-Holland, Amsterdam-New York, 1991, pp. 561-568. MR 1218218 |
| Reference:
|
[13] PETHO A.: Perfect powers in second order linear recurrences.J. Number Theory, 15 (1982), 5-13. MR 0666345 |
| Reference:
|
[14] PETHO A.: Perfect powers in second order recurrences.In: Topics in Classical Number Theory, Akademiai Kiado, Budapest, 1981, pp. 1217-1227. MR 0781182 |
| Reference:
|
[15] RIBENBOIM P.: Square classes of Fibonacci and Lucas numbers.Portugal. Math. 46 (1989), 159-175. Zbl 0687.10005, MR 1020964 |
| Reference:
|
[16] RIBENBOIM P., McDANIEL W. L.: Square classes of Fibonacci and Lucas sequences.Portugal. Math. 48 (1991), 469-473. MR 1147611 |
| Reference:
|
[17] RIBENBOIM P.: Square classes of $(a^n - l)/(a - 1)$ and $a^n +1$.Sichuan Daxue Xunebar, 26 (1989), 196-199. MR 1059704 |
| Reference:
|
[18] ROBBINS N.: On Fibonacci numbers of the form $PX^2$, where P is prime.Fibonacci Quart. 21 (1983), 266-271. MR 0723787 |
| Reference:
|
[19] ROBBINS N.: On Pell numbers of the form $PX^2$, where P is prime.Fibonacci Quart. 22 (1984), 340-348. MR 0766310 |
| Reference:
|
[20] SHOREY T. N., STEWART C. L.: On the Diophantine equation $ax^{2t}+ bx^ty + cy^2 = d$ and pure powers in recurrence sequences.Math. Scand. 52 (1983), 24-36. MR 0697495 |
| Reference:
|
[21] SHOREY T. N., STEWART C. L.: Pure powers in recurrence sequences and some related Diophatine equations.J. Number Theory 27 (1987), 324-352. MR 0915504 |
| Reference:
|
[22] WYLIE O.: In the Fibonacci series $F_1 = 1$, $F_2 = 1$, $F_{n+1} = F_n + F_{n-1}$ the first, second and twelfth terms are squares.Amer. Math. Monthly 71 (1964), 220-222. |
| . |
