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Fadwa S. Abu Muriefah, Florian Luca, and Alain Togbé.
On the Diophantine equation x² + 5a13b = yn.
Glasg. Math. J., 50(1):175–181, 2008. |
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S. Akhtari, A. Togbé, and P. G. Walsh.
On the equation aX4 - bY² = 2.
Acta Arith., 131(2):145–169, 2008. |
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M. A. Bennett, N. Bruin, K. Győry, and L. Hajdu.
Powers from products of consecutive terms in arithmetic progression.
Proc. London Math. Soc. (3), 92(2):273–306, 2006. |
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Michael A. Bennett.
The Diophantine equation (xk - 1)(yk - 1) = (zk - 1)t.
Indag. Math. (N.S.), 18(4):507–525, 2007. |
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Michael A. Bennett, Kálmán Győry, and Ákos Pintér.
On the Diophantine equation 1k + 2k + … + xk = yn.
Compos. Math., 140(6):1417–1431, 2004. |
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A. Bérczes, A. Pethő, and V. Ziegler.
Parameterized norm form equations with arithmetic progressions.
J. Symbolic Comput., 41(7):790–810, 2006. |
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Attila Bérczes and Attila Pethő.
Computational experiences on norm form equations with solutions
forming arithmetic progressions.
Glas. Mat. Ser. III, 41(61)(1):1–8, 2006. |
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A. Bremner and N. Tzanakis.
Lucas sequences whose 8th term is a square.
arXiv:math.NT/0408371 v2, 44 pages, 2004. |
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A. Bremner and N. Tzanakis.
On squares in Lucas sequences.
J. Number Theory, 124(2):511–520, 2007. |
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Andrew Bremner.
On the equation Y² = X5 + k.
Experiment. Math., 17(3):371–374, 2008. |
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Andrew Bremner.
A problem of Ozanam.
Proc. Edinburgh Math. Soc., 52(1):37–44, 2009. |
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N. Bruin, K. Győry, L. Hajdu, and Sz. Tengely.
Arithmetic progressions consisting of unlike powers.
Indag. Math. (N.S.), 17(4):539–555, 2006. |
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Nils Bruin.
The primitive solutions to x³ + y9 = z².
J. Number Theory, 111(1):179–189, 2005. |
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Nils Bruin.
Some ternary Diophantine equations of signature (n, n, 2).
In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 63–91. Springer, Berlin, 2006. |
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Nils Bruin and Michael Stoll.
Deciding existence of rational points on curves: an experiment.
Experiment. Math., 17(2):181–189, 2008. |
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Ralph H. Buchholz.
Triangles with three rational medians.
J. Number Theory, 97(1):113–131, 2002. |
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Ralph H. Buchholz and James A. MacDougall.
Cyclic polygons with rational sides and area.
J. Number Theory, 128(1):17–48, 2008. |
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Yann Bugeaud, Florian Luca, Maurice Mignotte, and Samir Siksek.
On perfect powers in Lucas sequences.
Int. J. Number Theory, 1(3):309–332, 2005. |
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Yann Bugeaud, Maurice Mignotte, and Samir Siksek.
Classical and modular approaches to exponential Diophantine
equations I: Fibonacci and Lucas perfect powers.
Ann. of Math. (2), 163(3):969–1018, 2006. |
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Yann Bugeaud, Maurice Mignotte, and Samir Siksek.
Classical and modular approaches to exponential Diophantine
equations II: The Lebesgue-Nagell equation.
Compos. Math., 142(1):31–62, 2006. |
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Yann Bugeaud, Maurice Mignotte, and Samir Siksek.
A multi-Frey approach to some multi-parameter families of
Diophantine equations.
Canad. J. Math., 60(3):491–519, 2008. |
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Yann Bugeaud, Maurice Mignotte, Samir Siksek, Michael Stoll, and Szabolcs
Tengely.
Integral points on hyperelliptic curves.
Algebra Number Theory, 2(8):859–885, 2008. |
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Imin Chen.
A Diophantine equation associated to X0(5).
LMS J. Comput. Math., 8:116–121 (electronic), 2005. |
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Imin Chen.
On the equation s² + y2p = α³.
Math. Comp., 77(262):1223–1227, 2008. |
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Imin Chen and Samir Siksek.
Perfect powers expressible as sums of two cubes.
J. Algebra, 322(3):638–656, 2009. |
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C. Chisholm and J. A. MacDougall.
Rational and Heron tetrahedra.
J. Number Theory, 121(1):153–185, 2006. |
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C. Chisholm and J. A. MacDougall.
Rational tetrahedra with edges in geometric progression.
J. Number Theory, 128(2):251–262, 2008. |
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Mihai Cipu.
Gröbner bases and Diophantine analysis.
J. Symbolic Comput., 43(10):681–687, 2008. |
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Mihai Cipu, Florian Luca, and Maurice Mignotte.
Solutions of the Diophantine equation xy + yz + zx = n!.
Glasg. Math. J., 50(2):217–232, 2008. |
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Henri Cohen.
Number Theory: Volume I: Tools and Diophantine Equations.
Springer, Berlin, 2007. |
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Gunther Cornelissen, Thanases Pheidas, and Karim Zahidi.
Division-ample sets and the Diophantine problem for rings of
integers.
J. Théor. Nombres Bordeaux, 17(3):727–735, 2005. |
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Robert S. Coulter, Marie Henderson, and Felix Lazebnik.
On certain combinatorial Diophantine equations and their connection
to Pythagorean numbers.
Acta Arith., 122(4):395–406, 2006. |
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A. Bremnerand Jean-Joël Delorme.
On equal sums of ninth powers.
Math. Comp, In Press, 2009. |
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Luis V. Dieulefait.
Solving Diophantine equations x4 + y4 = qzp.
Acta Arith., 117(3):207–211, 2005. |
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Shanshan Ding.
Smallest irreducible of the form x² - dy².
Int. J. Number Theory, 7 pages, 2007. |
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Konstantinos Draziotis and Dimitrios Poulakis.
Practical solution of the Diophantine equation
y² = x(x + 2apb)(x - 2apb).
Math. Comp., 75(255):1585–1593 (electronic), 2006. |
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Konstantinos Draziotis and Dimitrios Poulakis.
Solving the Diophantine equation y2.
Journal of Number Theory, 129(1):102 – 121, 2009. |
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Konstantinos A. Draziotis.
Integer points on the curve Y² = X³ ± pkX.
Math. Comp., 75(255):1493–1505 (electronic), 2006. |
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Edray Goins, Florian Luca, and Alain Togbé.
On the diophantine equation x ² + 2α5β13γ = y n .
In Algorithmic Number Theory, volume 5011 of Lecture Notes
in Computer Science, pages 430–442. Springer Berlin / Heidelberg, 2008. |
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K. Győry and Á. Pintér.
Almost perfect powers in products of consecutive integers.
Monatsh. Math., 145(1):19–33, 2005. |
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K. Győry and Á. Pintér.
Correction to the paper: ``Almost perfect powers in products of
consecutive integers''.
Monatsh. Math., 146(4):341, 2005. |
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K. Győry and Á. Pintér.
On the resolution of equations Axn - Byn = C in integers
x, y and n ≥ 3. I.
Publ. Math. Debrecen, 70(3-4):483–501, 2007. |
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Lajos Hajdu and Szabolcs Tengely.
Arithmetic progressions of squares, cubes and n-th powers.
arXiv:0707.0593, 10 pages, 2007. |
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Lajos Hajdu, Szabolcs Tengely, and Robert Tijdeman.
Cubes in products of terms in arithmetic progression.
Publ. Math. Debrecen, 74(1-2):215–232, 2009. |
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Robin Hartshorne and Ronald van Luijk.
Non-Euclidean Pythagorean triples, a problem of Euler, and
rational points on K3 surfaces.
Math. Intelligencer, 30(4):4–10, 2008. |
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Bo He and Alain Togbé.
On the number of solutions of Goormaghtigh equation for given x
and y.
Indag. Math. (N.S.), 19(1):65–72, 2008. |
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E. Herrmann, I. Járási, and A. Pethő.
Note on: ``The Diophantine equation xn = Dy² + 1'' by J. H.
E. Cohn.
Acta Arith., 113(1):69–76, 2004. |
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E. Herrmann, F. Luca, and P. G. Walsh.
A note on the Ramanujan-Nagell equation.
Publ. Math. Debrecen, 64(1-2):21–30, 2004. |
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Emanuel Herrmann and Attila Pethő.
S-integral points on elliptic curves. Notes on a paper of B.
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J. Théor. Nombres Bordeaux, 13(2):443–451, 2001. |
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Stephen P. Humphries and Kenneth W. Johnson.
Fusions of character tables and Schur rings of abelian groups.
Comm. Algebra, 36(4):1437–1460, 2008. |
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L. Hajdu K. Györy and A. Pinter.
Perfect powers from products of consecutive terms in arithmetic
progression.
145(4):845–864, 2009. |
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Tünde Kovács.
Combinatorial Diophantine equations—the genus 1 case.
Publ. Math. Debrecen, 72(1-2):243–255, 2008. |
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Shanta Laishram, T. N. Shorey, and Szabolcs Tengely.
Squares in products in arithmetic progression with at most one term
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Acta Arith., 135(2):143–158, 2008. |
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Dino Lorenzini and Thomas J. Tucker.
Thue equations and the method of Coleman-Chabauty.
arXiv:math.NT/0005186, 30 pages, 2000. |
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F. Luca, P. Stanica, and A. Togbé.
On a Diophantine equation of Stroeker.
Bull. Belg. Math. Soc. Simon Stevin, page 10, 2008. |
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F. S. Abu Muriefah, F. Luca, S. Siksek, and S. Tengely.
On the Diophantine equation x² + c = 2yn.
Int. J. Number Theory, 2008. |
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Á. Pintér.
On a class of Diophantine equations related to the numbers of cells
in hyperplane arrangements.
J. Number Theory, 129(7):1664–1668, 2009. |
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Ákos Pintér.
On the power values of power sums.
J. Number Theory, 125(2):412–423, 2007. |
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Bjorn Poonen, Edward F. Schaefer, and Michael Stoll.
Twists of X(7) and primitive solutions to x² + y³ = z7.
Duke Math. J., 137(1):103–158, 2007. |
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Samir Siksek and John E. Cremona.
On the Diophantine equation x² + 7 = ym.
Acta Arith., 109(2):143–149, 2003. |
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N. P. Smart.
Thue and Thue-Mahler equations over rings of integers.
J. London Math. Soc. (2), 56(3):455–462, 1997. |
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Nigel P. Smart.
The Algorithmic Resolution of Diophantine Equations,
volume 41 of London Mathematical Society Student Texts.
Cambridge University Press, Cambridge, 1998. |
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Sz. Tengely.
Note on the paper: ``An extension of a theorem of Euler'' by N.
Hirata-Kohno, S. Laishram, T. N. Shorey and R. Tijdeman.
Acta Arith., 134(4):329–335, 2008. |
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Szabolcs Tengely.
On the Diophantine equation x² + a² = 2yp.
Indag. Math. (N.S.), 15(2):291–304, 2004. |
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Szabolcs Tengely.
Effective Methods for Diophantine Equations.
PhD thesis, Leiden University, 2005. |
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Szabolcs Tengely.
Triangles with two integral sides.
Ann. Math. Inform., 34:89–95, 2007. |
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P. G. Walsh.
On a very particular class of Ramanujan-Nagell type equations.
Far East J. Math. Sci. (FJMS), 24(1):55–58, 2007. |
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Jahan Zahid.
Zeros of p-adic forms.
J. Number Theory, 129(10):2439–2456, 2009. |
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Huilin Zhu and Jianhua Chen.
Integral points on a class of elliptic curve.
Wuhan Univ. J. Nat. Sci., 11(3):477–480, 2006. |
