Research
Algebraic Number Theory, especially Diophantine equations.
Conferences
CIMPA/ICTP Summer research school in Benin
Conference on Diophantine mtuples and related problems
Selected PublicationsOn a pure ternary exponential Diophantine equation
 (With M. Le, H. Zhu), On a pure ternary Diophantine equation, Accepted to appear in Publicationes Mathematicae Debrecen.
 (with S. Yang), Proof of the Pinteger conjecture of Pomerance, Accepted to appear in the Journal of Number Theory.
 (With H. Zhu, M. Le, G. Soydan), On the exponential Diophantine equation x^{2} + 2^{a} p^{b} = y^{n}, Accepted to appear in Periodica Mathematica Hungarica.
 (with H. Godinho, D. Marques), On the Diophantine equation x^{2} + C = y^{n} for C =2^{a} 3^{b} 17^{c} and C =2^{a} 13^{b} 17^{c}. Acccepted to appear in Mathematica Slovaca.
 (with H . Godinho, T. Porto), On the Diophantine Equation v(v+1)=u(u+a)(u+2a). Accepted to appear in
Acta Mathematica Hungarica.
 (with A. Filipin, Y. Fujita ), The extendibility of Diophantine pairs I: the general case. Accepted to appear in Glas. Mat. Ser. III.
 (with B. He, S. Yang, W. Wu), The solution number of the Diophantine equations y^{2}=nx(Ax^{2}\pm C) . Accepted to appear in
The South Pacific Journal
of Pure and Applied Mathematics.

(with
S.
Yang,
W.
Wu), Diophantine equations involving normalized binomial midcoefficients.
Accepted to appear in Publicationes Mathematicae Debrecen.
 (with B. He, I. Pink, A. Pinter) On the Diophantine inequality X^{2}cXY^{2}+Y^{4}<= c+2 , Accepted to appear in Glas. Mat. Ser. III.
 A note on the Diophantine equation y^{2} =px(Ax^{2} +2) , Accepted to appear in Afrika Mathematika.

(with S. Yang, B. He),
On the solutions of the exponential
Diophantine equation a^{x}+ b^{y }=(m^{2}+1)^{z},
Quaestiones Mathematicae, 36 (2013), 119135.
 (with D. Marques), Fibonacci and Lucas numbers of the form 2^{a} + 3^{b} + 5^{c} . Proceedings of Japan Mathematics Academy, Ser. A . Proceedings of Japan Mathematics Academy, 89 Ser. A (2013) 4750.

(with
H. Godinho,
D. Marques), On
the Diophantine equation
x^{2} + 2^{α} 5^{β} 17^{γ}
= y^{n}.
Communications in Mathematics journal,
20 (2012)
8188.

(with D. Marques), On repdigits as
product of consecutive Fibonacci numbers.
Rendiconti dell' Istituto di Matematica dell' Universita' di
Trieste,
Volume 44 (2012), 393397.

(with Y. Fujita),
The extension of the D(k^{2})pair
{k^{2}, k^{2}+1}.
Periodica Mathematica Hungarica, Volume 65, Issue 1, September
2012, 7581.

(with T. Miyazaki), The
Diophantine equation (2am1)^{x}+ (2m)^{y }
=(2am+1)^{z},
International Journal of Number Theory,
Vol. 08, No. 08, (2012) 20352044.

(with
M. Le, H. Zhu), On the exponential Diophantine equation x^{2
}+ p^{2m }= 2y^{n}.
The Bulletin of the Australian
Mathematical Society,
Volume 86, Issue 02,
October 2012, 303  314.

(with D. Marques),
On the sum of powers of consecutive terms of a linear recurrence sequence. Bull Braz Math Soc.,
New Series 43(3), (2012) 397406.

(with A. Filipin, B. He)
On a family of twoparametric
D(4)triples. Glas. Mat. Ser. III, Vol. 47, No.1 (2012),
3151.

(with B. He)
On a family of Diophantine triples {k, A^{2}k+2A
,(A+1)^{2}k+2(A+1)} with two parameters II.
Periodica Mathematica Hungarica Vol. 64 (1), 2012, 110.

(with D. Marques),
A Diophantine equation involving Cnomial
coefficients.
EastWest J. of Mathematics, Vol. 13, No 1
(2011) 7579

(with Y. Fujita),
Uniqueness of the extension of the D(4k^{2})triple
{k^{2}4, k^{2}, 4k^{2}4}. NNTDM 17 (2011),
4, 42–49.

(with
A. Bajolet, B. Dupuy, F. Luca), On the Diophantine equation x^{4
} q^{4 }= py^{r}.
Publicationes Mathematicae Debrecen, 79/34
(2011) 269282.

(with P. Yuan),
On a variant of a Diophantine equation of
Cassels. Glas. Mat. Ser. III, Vol. 46, No.2 (2011), 325331.

(with D. Marques),
On terms of linear recurrence sequences
with only one distinct block of digits. Colloquium Mathematicum
124 (2011), 145155.

(with B. He, O. Kihel),
Solutions of a class of quartic Thue inequalities.
Computers and Mathematics
with Applications 61 (2011) 2914–2923.

(with M. Cipu, M. Mignotte),
On the size of the intersection
of two Lucas sequences of Distinct type II.
Science China Mathematics 54 (2011) 12991316.

(with K, A. Broughan, M. J. Gonzalez, R. H. Lewis, F. Luca, J. M.
Huguet) There are no multiplyperfect Fibonacci numbers.
INTEGERS 11, (2011), 363397.

(with S. Yang),
On a conjecture of the power series
coefficients of the function U(n, x). Annales des sciences
mathématiques du Québec, 35, no. 1 (2011), 13740.

(with B. He)
On the positive integer solutions of the
exponential Diophantine equation a^{x}+(3a^{2}1)^{y}=(4a^{2}1)^{z}.
Advances in Mathematics (Chinese) Vol. 40, No. 2, (2011),
227234.

(with B. He, P. G. Walsh)
On the size of the intersection of
two Lucas sequences of distinct type. Annales des
sciences mathématiques du Québec, 35, no. 1 (2011), 3161.

(with J. Luo, P. Yuan),
On some equations related to Ma's
conjecture. INTEGERS 11A, (2011), Article 27.

(with S. Yang, B. He),
Diophantine equations with products of consecutive values of a
quadratic polynomial.,
Journal of Number Theory, 131, no. 10, (2011)
18401851.

(with B. He)
On the D(1) triple {1, k^{2}+1, k^{2}+2k+2}
and its unique D(1)extension. Journal of Number Theory,
Volume 131, Issue 1, (2011) 120137.

(with D. Marques),
On the sum of powers of two consecutive
Fibonacci numbers, Proceedings of Japan Mathematics Academy,
Ser A, December 2010, 174176.

(with S. Yang, B. He), A note on the Diophantine equation a^{x}
 b^{y}=c. Mathematica Scandinavica Volume
107, Number 2, (2010) 161173.

(with B. He, M. Ulas)
On the Diophantine equation z^{2}
= f(x)^{2} ± f(y)^{2} II. The Bulletin of
the Australian Mathematical Society 82 (2010) 187204.

(with B. He, P. Yuan)
On the Diophantine equation X^{2
} (p^{2m} + 1)Y^{6 }= p^{2m}.
Functiones et Approximatio Commentarii Mathematici
Volume 43, Number 1 (2010), 3144.

(with A. Filipin, B. He)
On the D(4)triple {F_{2k}, F_{2k+6},
4F_{2k+4}}.
Fibonacci Quart. 48 (2010), no. 3, 219–227.

(with D. Marques)
Perfect Powers among Fibonomial Coefficients.
C. R. Acad. Sci. Paris, Ser. I 348 (2010) 717–720.

(with B. He)
On the number of solutions of the Diophantine
equation
ax^{m
} by^{n}
= c.
The Bulletin of the Australian Mathematical Society, (2010), 81
177185.

(M. Ulas)
On the Diophantine equation z^{2} = f(x)^{2}
± f(y)^{2}. Publicationes Mathematicae
Debrecen 76/12 (2010), 183201.

(with O. Kihel, F. Luca)
Variants of the Diophantine Equation
n! + 1 = y^{2}. Portugaliae Mathematica,
Volume 67, Issue 1 (2010), 111.

(with F. Luca, P. Stanica)
On a Diophantine equation of
Stroeker.
Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 1–8.

(with F. Luca)
On the Diophantine Equation x^{4 } q^{4
}= py^{3}. Rocky Mountain Journal of
Mathematics, vol. 40, no. 3, (2010) 9951008.

(with B. He)
A remark on the generalized RamanujanNagell
equation x^{2}  D = k^{n} Ann. Sci. Math.
Québec 33 (2009), no 2, 165169.

(with A. Filipin)
On the family of Diophantine triples {k+2,
4k, 9k+6}.
Acta Mathematica Academiae Paedagogicae Nyíregyháziensis,
Vol. 25, No. 2, (2009), 145153.

(with B. He, B. Jadrijevic)
Solutions of a class of quartic
Thue inequalities. Glas. Mat. Ser. III,
Vol. 44
(64) (2009), 309 – 321.

(with F. Luca, S. Tengely)
On the Diophantine Equation x^{2}
+ C = 4y^{n}. Ann. Sci. Math. Québec 33
(2009), no 2, 171184.

(with B. He)
The Diophantine equation n^{x }+ (n+1)^{y}
= (n+2)^{z} revisited. The
Glasgow Mathematical Journal, Volume 51, Issue 03, September
2009, 659667.

(with S. Yang, B. He),
A 2×2 Lattice spacetime code of the
highest rank. Proceedings of the American
Mathematical Society, 137 (2009), 36013607.

On the positive integral solutions of the Diophantine equation x^{3
}+ by + 4 – xyz = 0.
African Diaspora Journal of Mathematics,
8 (2009), No. 1, 8189.

(with B. He)
On a family of Diophantine triples {k, A^{2}k+2A
,(A+1)^{2}k+2(A+1)} with two parameters. Acta
Mathematica Hungarica., 124 (12) (2009), 99113.

(with F. Luca)
On the Diophantine equation x^{2} + 2^{a}
13^{b} = y^{n}. Colloquium Mathematicum,
116 (2009), 139146.

(with S. Akhtari, P. G. Walsh)
Addendum on the equation aX^{4
} bY^{2}=2. Acta Arithmetica
137 (2009), 199202.

(with B. He)
On the family of Diophantine triples {k+1, 4k,
9k+3}., Periodica Mathematica Hungarica, 58 (1)
(2009), 5970.

(with B. He, G. P. Walsh)
On the Diophantine equation X^{2
}– (2^{2m} +1)Y^{4}=2^{2m}.
Publ. Math. Debrecen, 73/34 (2008) 417420.

(with B. He)
Simultaneous Pellian equations with a single or
no solution, Acta Arith. 134 (2008), 369380.

(with B. He)
On the number of solutions of Goormaghtigh
equation for given x and y, Indag. Mathem., N.S., 19 (1)
(2008), 6572.

On the solutions of a parametric family of cubic Thue equations.
Bull Braz Math Soc, New Series 39 (4) (2008), 537554.

(with F. Luca)
On the positive integral solutions of the
Diophantine equation x^{3 }+ by + 1  xyz=0. Bull.
Malays. Math. Sci. Soc. (2) 31 (2) (2008), 129–134.

(with F. Luca)
On the Diophantine equation x^{2} + 2^{a}
5^{b} = y^{n}. Int. J. Number Theory, 4, (6)
(2008), 973979.

(with E. Goins and F. Luca)
On the Diophantine Equation x^{2}
+ 2^{α} 5^{β} 13^{γ} = y^{n}.
ANTS VIII Proceedings: A.J. van der Poorten and A. Stein (eds.),
ANTS VIII, Lecture Notes in Computer Science 5011 (2008), 430442.

(with F. Luca)
On binary palindromes of the form 10^{n} ±
1. C. R. Acad. Sci. Paris, Ser. I 346 (2008) 487–489.

(with F. Luca)
On the numbers of the form ± x^{2 }± y! Diophantine Equation, Editor: N. Saradha, Narosa Publishing House,
(2008), pp. 135149.

(with S. Akhtari, P.G. Walsh)
On the equation aX^{4}  bY^{2}
= 2. Acta Arith. 131 (2008), 145169.

(with F. S. Abu Muriefah and F. Luca)
On the Diophantine equation
x^{2} + 5^{a} 13^{b} = y^{n}.
The Glasgow Mathematical Journal, Volume 50, Issue 01, January 2008, pp 175181.

(with F. Luca)
On the Diophantine equation x^{2} + 7^{2k}
= y^{n}. The Fibonacci Quarterly Vol. 54.4 (2007)
322326.

(with E. Goins)
On Pythagorean Quadruplets.
International Journal of Pure and Applied Mathematics, Volume 35,
No. 3 (2007), 363372.

A parametric family of sextic Thue equations.
Acta Arith. 125 (2006), 347361.

A Note on the Diophantine Equation x! + A = y^{2}II.
International Journal of Applied Mathematics & Statistics, Vol.
6,
No. D06 (2006), 2532.

Complete Solutions of a Family of Cubic Thue Equations,
Journal de Theorie des Nombres de Bordeaux 18 (2006), 285298.

(with M. Bennett, G. P. Walsh)
A generalization of a theorem
of Bumby on quartic Diophantine equations. International
Journal of Number Theory, Vol. 2, No. 2 (June 2006) 195206.

A Note on the Diophantine Equation x^{2} + D = p^{n}
, RJooiA, Transactions on Mathematics, Spring 2006, pp. 125129.

On the solutions of a family of quartic Thue equations II.
C. R. Math. Rep. Acad. Sci. Canada Vol. 28. (1), 2006 pp. 2432.

A Note on the Diophantine Equation x! + A = y^{2}.
International Journal of Pure and Applied Mathematics, Volume 26,
No. 4 (2006), 565571.

(With P. M. Voutier, G. P. Walsh)
Solving a family of Thue
equations with an application to the equation x^{2} – Dy^{4}
= 1. Acta Arithmetica 120 (2005), 395

(with C. Heuberger and V. Ziegler)
Automatic solution of families
of Thue equations and an example degree 8, J. Symbolic
Computation
38
(2004), Issue 3, 11451163.

A Parametric Family of Cubic Thue Equations,
J. Number Theory 107 (2004), 6379.

On the solutions of a family of sextic equations,
Number Theory for the Millennial, Bruce Berndt, et. al., editors,
A.K. Peters Ltd, 2002, Volume III, 285299.

On the solutions of a family of quartic equations,
Math. Comp. 69 (2000), 839849.

On binary quadratic forms,
Proceedings of the 11^{th} Conference of ACMS, 1997,
125135.
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