ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn
Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 175-181

Voir la notice de l'article provenant de la source Cambridge University Press

In this note, we find all the solutions of the Diophantine equation x2 + 5a 13b = yn in positive integers x, y, a, b, n≥ 3 with x and y coprime.
DOI : 10.1017/S0017089507004028
Mots-clés : 11D61, 11Y50
MURIEFAH, FADWA S. ABU; LUCA, FLORIAN; TOGBÉ, ALAIN. ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 175-181. doi: 10.1017/S0017089507004028
@article{10_1017_S0017089507004028,
     author = {MURIEFAH, FADWA S. ABU and LUCA, FLORIAN and TOGB\'E, ALAIN},
     title = {ON {THE} {DIOPHANTINE} {EQUATION} x2 + 5a 13b = yn},
     journal = {Glasgow mathematical journal},
     pages = {175--181},
     year = {2008},
     volume = {50},
     number = {1},
     doi = {10.1017/S0017089507004028},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507004028/}
}
TY  - JOUR
AU  - MURIEFAH, FADWA S. ABU
AU  - LUCA, FLORIAN
AU  - TOGBÉ, ALAIN
TI  - ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn
JO  - Glasgow mathematical journal
PY  - 2008
SP  - 175
EP  - 181
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507004028/
DO  - 10.1017/S0017089507004028
ID  - 10_1017_S0017089507004028
ER  - 
%0 Journal Article
%A MURIEFAH, FADWA S. ABU
%A LUCA, FLORIAN
%A TOGBÉ, ALAIN
%T ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn
%J Glasgow mathematical journal
%D 2008
%P 175-181
%V 50
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507004028/
%R 10.1017/S0017089507004028
%F 10_1017_S0017089507004028

[1] 1.Arif, S. A. and Abu Muriefah, F. S., On the Diophantine equation x 2 + 2k = y n, Internat. J. Math. Math. Sci. 20 (1997), 299–304. Google Scholar | DOI

[2] 2.Arif, S. A. and Muriefah, F. S. Abu, The Diophantine equation x 2 + 3m = y n, Internat. J. Math. Math. Sci. 21 (1998), 619–620. Google Scholar | DOI

[3] 3.Arief, S. A. and Muriefah, F. S. Abu, On a Diophantine equation, Bull. Austral. Math. Soc. 57 (1998), 189–198. Google Scholar

[4] 4.Abu Muriefah, F. S. and Arif, S. A., The Diophantine equation x 2 + 52k+1 = y n, Indian J. Pure Appl. Math. 30 (1999), 229–231. Google Scholar

[5] 5.Arif, S. A. and Muriefah, F. S. Abu, On the Diophantine equation x 2 + q 2k+1 = y n, J. Number Theory 95 (2002), 95–100. Google Scholar | DOI

[6] 6.Abu Muriefah, F. S., On the diophantine equation x 2 +52k = y n, Demonstratio Mathematica 319 (2) (2006), 285–289. Google Scholar

[7] 7.Muriefah, F. S. Abu and Bugeaud, Y., The Diophantine equation x 2 + c = y n: a brief overview, Rev. Colombiana Math. 40 (2006), 31–37. Google Scholar

[8] 8.Bilu, Yu., Hanrot, G. and Voutier, P. M., Existence of primitive divisors of Lucas and Lehmer numbers, (Appendix by M. Mignotte), J. reine angew. Math. 539 (2001), 75–122. Google Scholar

[9] 9.Bugeaud, Y., Mignotte, M. and Siksek, S., Classical and modular approaches to exponential Diophantine equations. II. The Lebesgue-Nagell equation, Composition Math. 142 (2006), 31–62. Google Scholar | DOI

[10] 10.Cohn, J. H. E., The Diophantine equation x 2 + c = y n, Acta Arith. 65 (1993), 367–381. Google Scholar | DOI

[11] 11.Ko, C., On the Diophantine equation x 2 = y n +1, xy 0, Sci. Sinica 14 (1965), 457–460. Google Scholar

[12] 12.Le, M., An exponential Diophantine equation, Bull. Austral. Math. Soc. 64 (2001), 99–105. Google Scholar | DOI

[13] 13.Le, M., On Cohn's conjecture concerning the Diophantine equation x 2 + 2m = y n, Arch. Math. (Basel) 78 (2002), 26–35. Google Scholar | DOI

[14] 14.Lebesgue, V. A., Sur l'impossibilité en nombres entiers de l'équation x m = y 2+1, Nouv. Annal. des Math. 9 (1850), 178–181. Google Scholar

[15] 15.Luca, F., On a Diophantine Equation, Bull. Austral. Math. Soc. 61 (2000), 241–246. Google Scholar | DOI

[16] 16.Luca, F., On the equation x 2 + 2a \cdot 3b = y n, Int. J. Math. Math. Sci. 29 (2002), 239–244. Google Scholar | DOI

[17] 17.Luca, F. and Togbé, A. On the equation x 2 + 2a · 5b = y n, Int. J. Number Theory, to appear. Google Scholar

[18] 18.Mignotte, M. and Weger, B. M. M. de, On the Diophantine equations x 2+74 = y 5 and x 2+86=y5, Glasgow Math. J. 38 (1996), 77–85. Google Scholar | DOI

[19] 19.Pink, I., On the diophantine equation x 2 + 2α. 3β. 5γ. 7δ =y n, Publ. Math. Debrecen 70/1–2 (2006), 149–166. Google Scholar

[20] 20.Tengely, Sz., On the Diophantine equation x 2 + a 2 = 2y p, Indag. Math. (N.S.) 15 (2004), 291–304. Google Scholar | DOI

Cité par Sources :