[1] Muriefah, F.S.A.:
On the Diophantine equation $x^2+5^{2k}=y^n$. Demonstratio Mathematica 319/2 2006 285–289
Zbl 1100.11013
[4] Arif, S.A., Muriefah, F.S.A.:
The Diophantine equation $x^2+q^{2k}=y^n$. Arab. J. Sci. Sect. A Sci. 26 2001 53–62
MR 1829921
[5] Arif, S.A., Muriefah, F.S.A.:
On the Diophantine equation $x^2+2^k=y^n$ II. Arab J. Math. Sci. 7 2001 67–71
MR 1940290 |
Zbl 1010.11021
[7] Bennett, M.A., Ellenberg, J.S., Ng, Nathan C.: The Diophantine equation $A^4+2^dB^2=C^n$. submitted
[9] Bérczes, A., Brindza, B., Hajdu, L.:
On power values of polynomials. Publ. Math. Debrecen 53 1998 375–381
MR 1657483
[10] Bérczes, A., Pink, I.:
On the diophantine equation $x^2+p^{2k}=y^n$. Archiv der Mathematik 91 2008 505–517
MR 2465869 |
Zbl 1175.11018
[11] Bilu, Y., Hanrot, G., Voutier, P.M.:
Existence of primitive divisors of Lucas and Lehmer numbers. With an appendix by M. Mignotte. J. Reine Angew. Math. 539 2001 75–122
MR 1863855 |
Zbl 0995.11010
[12] Bugeaud, Y.:
On the diophantine equation $x^2-p^m=\pm y^n$. Acta Arith. 80 1997 213–223
MR 1451409
[13] Bugeaud, Y., Mignotte, M., Siksek, S.:
Classical and modular approaches to exponential and diophantine equations II. The Lebesque-Nagell equation. Compos. Math. 142/1 2006 31–62
DOI 10.1112/S0010437X05001739 |
MR 2196761
[14] Bugeaud, Y., Muriefah, F.S. Abu:
The Diophantine equation $x^2+c=y^n$: a brief overview. Revista Colombiana de Matematicas 40 2006 31–37
MR 2286850
[15] Bugeaud, Y., Shorey, T.N.:
On the number of solutions of the generalized Ramanujan-Nagell equation. J. reine angew. Math. 539 2001 55–74
MR 1863854 |
Zbl 0995.11027
[16] Cangül, I.N., Demirci, M., Soydan, G., Tzanakis, N.:
On the Diophantine equation $x^2 + 5^a11^b = y^n$. Funct. Approx. Comment. Math. 43 2010 209–225
MR 2767170
[17] Cangül, N., Demirci, M., Luca, F., Pintér, Á., Soydan, G.:
On the Diophantine equation $x^2 + 2^a11^b = y^n$. Fibonacci Quart. 48 2010 39–46
MR 2663418
[18] Carmichael, R.D.:
On the numerical factors of the arithmetic forms $ \alpha ^{n} \pm \beta ^{n} $. Ann. Math. (2) 15 1913 30–70
MR 1502458
[21] Cohn, J.H.E.:
The diophantine equation $x^2+C=y^n$. Acta Arith. 65 1993 367–381
MR 1259344
[23] Ellenberg, J.S.:
Galois representations to $\mathbb {Q}$-curves and the generalized Fermat Equation $A^4+B^2=C^p$. Amer. J. Math. 126 (4) 2004 763–787
MR 2075481
[24] Goins, E., Luca, F., Togbe, A.:
On the Diophantine Equation $x^2 + 2^{\alpha }5^{\beta }13^{\gamma } = y^n$. A.J. van der Poorten, A. Stein (eds.)ANTS VIII Proceedings ANTS VIII, Lecture Notes in Computer Science 5011 2008 430–432
MR 2467863 |
Zbl 1232.11130
[25] Győry, K., Pink, I., Pintér, Á.:
Power values of polynomials and binomial Thue-Mahler equations. Publ. Math. Debrecen 65 2004 341–362
MR 2107952 |
Zbl 1064.11025
[26] Le, M.:
On Cohn’s conjecture concerning the diophantine equation $x^2+2^m=y^n$. Arch. Math. Basel 78/1 2002 26–35
MR 1887313 |
Zbl 1006.11013
[28] Lebesgue, V.A.: Sur l’impossibilité en nombres entier de l’equation $x^m=y^2+1$. Nouvelle Annales des Mathématiques (1) 9 1850 178–181
[29] Ljunggren, W.:
Über einige Arcustangensgleichungen die auf interessante unbestimmte Gleichungen führen. Ark. Mat. Astr. Fys. 29A 1943 No. 13
MR 0012090 |
Zbl 0028.10904
[33] Luca, F., Togbe, A.:
On the Diophantine equation $x^2 + 7^{2k} = y^n$. Fibonacci Quarterly 54 2007 322–326
MR 2478616 |
Zbl 1221.11091
[35] Mignotte, M., Weger, B.M.M de:
On the equations $x^2+74=y^5$ and $x^2+86=y^5$. Glasgow Math. J. 38/1 1996 77–85
MR 1373962
[38] Muriefah, F.S.A., Luca, F., Togbe, A.:
On the diophantine equation $x^2+5^a13^b=y^n$. Glasgow Math. J. 50 2008 175–181
MR 2381741
[39] Nagell, T.: Sur l’impossibilité de quelques équations a deux indeterminées. Norsk. Mat. Forensings Skifter 13 1923 65–82
[40] Nagell, T.:
Contributions to the theory of a category of diophantine equations of the second degree with two unknowns. Nova Acta Reg. Soc. Upsal. IV Ser. 16, Uppsala 1955 1–38
MR 0070645
[41] Pink, I.:
On the diophantine equation $x^2+2^{\alpha }3^{\beta }5^{\gamma }7^{\delta }=y^n$. Publ. Math. Debrecen 70/1–2 2007 149–166
MR 2288472 |
Zbl 1121.11028
[44] Saradha, N., Srinivasan, A.:
Solutions of some generalized Ramanujan-Nagell equations via binary quadratic forms. Publ. Math. Debrecen 71/3–4 2007 349–374
MR 2361718 |
Zbl 1164.11020
[45] Schinzel, A., Tijdeman, R.:
On the equation $y^m=P(x)$. Acta Arith. 31 1976 199–204
MR 0422150
[46] Shorey, T.N., van der Poorten, A.J., Tijdemann, R., Schinzel, A.: Applications of the Gel’fond-Baker method to Diophantine equations. Transcendence Theory: Advances and Applications Academic Press, London-New York, San Francisco 1977 59–77
[47] Shorey, T.N., Tijdeman, R.:
Exponential Diophantine equations. Cambridge Tracts in Mathematics, 87. Cambridge University Press, Cambridge 1986 x+240 pp.
MR 0891406 |
Zbl 0606.10011
[48] Tengely, Sz.:
On the Diophantine equation $x^2+a^2=2y^p$. Indag. Math. (N.S.) 15 2004 291–304
MR 2071862