| Title:
|
Common terms in binary recurrences (English) |
| Author:
|
Orosz, Erzsébet |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
57-61 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to prove that the common terms of linear recurrences $M(2a,-1,0,b)$ and $N(2c,-1,0,d)$ have at most $2$ common terms if $p=2$, and have at most three common terms if $p>2$ where $D$ and $p$ are fixed positive integers and $p$ is a prime, such that neither $D$ nor $D+p$ is perfect square, further $a,b,c,d$ are nonzero integers satisfying the equations $a^2-Db^2=1$ and $c^2-(D+p)d^2=1$. (English) |
| Keyword:
|
Pell equation |
| Keyword:
|
binary sequences |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| MSC:
|
11D09 |
| MSC:
|
95U50 |
| idZBL:
|
Zbl 1132.11007 |
| idMR:
|
MR2298914 |
| . |
| Date available:
|
2009-12-29T09:20:24Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137484 |
| . |
| Reference:
|
[1] Bennett M. A.: On the number of solutions of simultaneous Pell equations., J. Reine Angew. Math., 498 (1998), 173–199. Zbl 1044.11011, MR 1629862 |
| Reference:
|
[2] Binz J.: Elemente der Math., 35 (1980), 155. |
| Reference:
|
[3] Hirsch M. D.: Additive sequences., Math. Mag., 50 (1977), 262. Zbl 0378.10006, MR 1572238, 10.2307/2689536 |
| Reference:
|
[4] Kiss P.: On Common terms of linear recurrences., Acta Math. Acad. Sci. Hungar. 40 (1–2), (1982), 119–123. Zbl 0508.10006, MR 0685998, 10.1007/BF01897310 |
| Reference:
|
[5] Kiss P.: Közös elemek másodrendű rekurzív sorozatokban.. Az egri Ho Si Minh Tanárképző Főiskola füzetei XVI. (1982), 539–546. |
| Reference:
|
[6] Kiss P.: Differences of the terms of linear recurrences., Studia Scientiarum Mathematicarum Hungarica 20 (1985), 285–293. Zbl 0628.10008, MR 0886031 |
| Reference:
|
[7] Liptai K.: Közös elemek másodrendű rekurzív sorozatokban., Acta. Acad. Pead. Agriensis, Sect. Math., 21 (1994), 47–54. |
| Reference:
|
[8] Mátyás F.: On common terms of second order linear recurrences., Mat. Sem. Not. (Kobe Univ. Jappan), 9 (1981), 89–97. MR 0633999 |
| Reference:
|
[9] Mignotte M.: Intersection des images de certains suites recurrentes lineaires., Theoretical Comput. Sci, 7 (1978), 117–122. MR 0498356, 10.1016/0304-3975(78)90043-9 |
| Reference:
|
[10] Mordell L. J.: Diophantine equations., Acad. Press, London, (1969), 270. Zbl 0188.34503, MR 0249355 |
| Reference:
|
[11] Revuz G.: Equations deiphanties exponentielles., Bull. Soc. Math. France, Mém., 37 (1974), 139–156. MR 0369249 |
| Reference:
|
[12] Schlickewei H. P., Schmidt W. M.: Linear equations in members of recurrence sequences., Ann. Scuola Norm. Sup. Pisa Cl. Sci. 20 (1993), 219–246. Zbl 0803.11010, MR 1233637 |
| Reference:
|
[13] Stewart C. L.: On divisors of terms of linear recurrence sequences., J. Reine Angew, Math., 333 (1982), 12–31. Zbl 0475.10009, MR 0660783 |
| . |
