### Conferences

CIMPA/ICTP Summer research school in Benin

Conference on Diophantine m-tuples and related problems

African School of Mathematics in Cape Verde

Conference on Diophantine m-tuples and related problems II

### Publications

- (with S. Rihane, B. Faye, F. Luca),
*An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers*Accepted to appear in Annales Mathematicae et Informaticae.*.* - (with S. Rihane, B. Faye, F. Luca),
. Accepted to appear in Turk J Math.**On the exponential equation P**^{x}_{n}**+P**^{x}_{n+1}**=P**_{m} - (with Eric Bravo, Carlos Gomez, Bir Kafle, F. Luca),
*On a conjecture concerning the multiplicity of the Tribonacci sequence**.*Accepted to appear in Colloquium Mathematicum. - (with B. He, J. Odjoumani),
, Accepted to appear in Journal of Number Theory.*On a class of quartic Thue equations with three parameters* - (with F. Luca, V. Togan),
, Accepted to appear in Annales Mathematicae et Informaticae.*On the X-coordinates of Pell equations which are rep-digits, II* - (with C. Adegbindin, F. Luca),
Accepted to appear in Bulletin of the Malaysian Mathematical Sciences Society.*Pell and Pell-Lucas numbers as sums of two repdigits.* - (with Y. Bilu, M. Diego),
. Accepted to appear in Journal of Number Theory.*Generalized Cullen Numbers in Linear Recurrence Sequences* - (with B. Kafle, F. Luca),
. Accepted to appear in Boletín de la Sociedad Matemática Mexicana.**x-coordinates of Pell equations which are Lucas numbers** - (with B. Kafle, F. Luca),
. Accepted to appear in Periodica Mathematica Hungarica.**x-coordinates of Pell equations which are Tribonacci numbers II** - (with B. Kafle, F. Luca),
. Accepted to appear in Mathematica Bohemica.**Lucas Factoriangular numbers** - (with B. V. Normenyo, F. Luca),
. Accepted to appear in Boletín de la Sociedad Matemática Mexicana.**Repdigits as sums of four Pell numbers** - (with S. Yang, F. Luca),
. Accepted to appear in Mathematica Bohemica.*On a Divisibility Problem* - (with B. He, K. Pu, R. Shen),
*A note on the regularity of the Diophantine pair {k, 4k**+-4}**.*Accepted to appear in Journal de Théorie des Nombres de Bordeaux. - (with F. Luca, J. Odjoumani),
*Pell Factoriangular numbers**.*Accepted to appear in*Inst. Math. Beograd*. - (with S. Rihane, M. Hernane),
. Colloquium Mathematicum 156 (2019). 273-285.*On Diophantine triples of Pell numbers* - (with B. Normenyo, F. Luca),
*Repdigits as sums of three Lucas number**.*Colloquium Mathematicum 156 (2019). 255-285. - (with B. He, V. Ziegler),
. Transactions of the American Mathematical Society, Volume 371, Number 9, May 2019, Pages 6665–6709.*There is no Diophantine Quintuple* - (with S. Subburam),
. Acta Mathematica Hungarica, 157(1), (2019) 1-9.*On the Diophantine equation y*^{n}= f(x)/g(x) - (with J. Odjoumani, V. Ziegler),
. Publicationes Mathematicae Debrecen, 2019 / 94 / 1-2 (1).*On a family of biquadratic fields that do not admit a unit powerintegral basis* - (with Z. Zhang),
. The Bulletin of the Australian Mathematical Society, Volume 99, Issue 1 February 2019, pp. 34-41.*Perfect Powers that are sums of two powers of Fibonacci numbers* - (with S. Rihane, M. Hernane),
Turk J Math, 43, (2019), 207-223.*The x-coordinates of Pell equations and Padovan numbers.* - (with B. Kafle, F. Luca),
. The Fibonacci Quarterly 56 (2018), no. 4, 325–328.**Triangular repblocks** - (with S. Rihane, M. Hernane, F. Luca),
Hardy-Ramanujan Journal 41 (2018), 8-17.*On Pillai’s problem with Pell numbers and powers of 2.* - (with Z. Zhang),
. Glas. Mat. Ser. II, Vol. 53 No 2, (2018) 221-228.*On the Ramanujan-Nagell type Diophantine equations x*^{2}+ Ak^{n}=B II - (with B. V. Normenyo, F. Luca),
**Repdigits as sums of**. Journal of Integer Sequences, 21 (2018), Article 18.7.7.*four Fibonacci or Lucas numbers* - (with B. Normenyo, F. Luca),
Periodica Mathematica Hungarica, December 2018, Volume 77, Issue 2, pp 318–328.*Repdigits as sums of three Pell numbers.* - (with N. Irmak),
. The Notes on Number Theory and Discrete Mathematics, Vol 24, 2018, No. 3, 95-102.*On repdigits as product of consecutive Lucas Numbers* - (with Z. Zhang),
. Glas. Mat. Ser. II, Vol. 53 No 1, (2018) 43-50.*On the Ramanujan-Nagell type Diophantine equations x*^{2}+ Ak^{n}=B - (with S. E. Rihane, M. O. Hernane),
The Fibonacci Quarterly, 56 (2018), no. 1, 63-74.*On D(4)-Diophantine triples of Fibonacci numbers.* - (with F. Luca),
Mathematica Scandinavica, Vol. 122, No. 1 (2018) 18-30.*On the x-coordinates of Pell equations which are Fibonacci numbers.* - (with B. He, A. Pinter, S. Yang),
*Another generalization of a theorem of Baker and Davenport**.*Number Theory**182**(2018), 325-343. - (with A. Bayad, A. Dossavi-Yovo, A. Filipin),
*On the extensibility of the D(4)-triple {k-2, k+2, 4k} over Gaussian integers**. Notes on Number Theory and Discrete Mathematics,*Vol. 23, 2017, No. 3, 1–26. - (with L. Tan, V. Vijayarajan, N. Chimitt, J. Jiang),
2017 IEEE Ubiquitous Computing, Electronics and Mobile Communications (UEMCON 2017), pp. 225-231, Columbia University, New York City, NY, October 2017.*Channel sparsity-aware recursive least squares algorithms for nonlinear system modeling and active noise control.* - (with F. Luca, A. Montejano, L. Szalay),
. Acta Arithmetica, 179.1 (2017), 25-35.*On the X-coordinates of Pell equations which are Tribonacci numbers* - (with Nicholas Chimitt, William Misch, Li Tan, and Jean Jiang),
. 2017 IEEE International Conference on Electro/Information Technology, pp. 166-170, University of Nebraska, Lincoln, Nebraska, May 2017.*Comparative Study of Simple Feature Extraction for Single-Channel EEG Based Classification* - (with G. Soydan, M. Demirci, I. Cangul),
J. Appl. Math. Stat., Vol. 56, Issue No. 6, Year 2017.*On the conjecture of Jesmanowicz.* - (with B. Kafle, F. Luca),
. Colloquium Mathematicum 149 (2017), 75-85.*On the x-coordinates of Pell equations which are Fibonacci numbers II* - (with A. Dossavi-Yovo, B. He),
*The extensibility of the D(**k)-triple {k**1,k, 4k**1}**.*Afrika Matematika Volume 28, Issue 3-4, June 2017, 563-574. - (with S. Subburam),
. Accepted to appear in Afrika Matematika, Volume 28, Issue 1-2, March 2017, 9-21.*On the Diophantine equation ax*^{3 }+ by + c – xyz = 0 - (with A. Bayad, M. O. Hernane),
. Accepted to appear in Functiones et Approximatio Commentarii Mathematici, Volume 55, Number 1 (2016), 113-130.*On extended Eulerian numbers* - (with S. Yang),
. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 1, pp. 23-31 (2016).*A note of three prime representation problem* - (with A. Bayad, A. Filipin),
. Acta Math. Hungar, Volume 148, Issue 2, April 2016, pp 312–327.*Extension of a parametric family of Diophantine triples in Gaussian integers* - (with A. Dossavi-Yovo, F. Luca),
. Publicationes Mathematicae Debrecen, 2016 / 88 / 3-4 (9).*On the x-coordinates of Pell equations which are rep-digits* - (with B. He, F. Luca),
. Acta Arithmetica 175 (2016), 57-70.*Diophantine triples of Fibonacci* - (with Z. Zhang),
. Glas. Mat. Ser. III, 51, No.1 (2016), 17-22.*On two Diophantine equations of Ramanujan-Nagell type* - (with S. Yang),
. The Ramanujan Journal, June 2016, Volume 40, Issue 2, pp 245–255.*On the estimates of the upper and lower bounds of Ramanujan primes* - (with S. Subburam),
. Period Math Hung, March 2016, Volume 72, Issue 1, pp 43–49.*On Erdos-Straus Conjecture* - (with T. Miyazaki, P. Yuan),
. Acta Mathematica Hungarica, Volume 149, Issue 1, June 2016, 1-9.*On the Diophantine equation a*^{x}+b^{y}=(a+2)^{z} - (with Godinho, D. Marques),
*On**the Diophantine equation**x*^{2}+*C*for C =2*= y*^{n}^{a}3^{b}17^{c}and C =2^{a}13^{b}17^{c}. Mathematica Slovaca, Volume 66, Issue 3 (June 2016), 565–574. - (with Jones, D. Marques),
. Indian Journal of Mathematics, Volume 57, No. 2, 2015, 151-164.*On terms of Lucas sequences with only one distinct digit* - (with B. He, A. Pinter),
. Proc. Amer. Math. Soc.*On simultaneous Pell equations and related Thue equations***143**(2015), 4685-4693. - (With H. Zhu, M. Le, G. Soydan),
. Periodica Mathematica Hungarica, June 2015, Volume 70, Issue 2, 233-247.*On the exponential Diophantine equation x*^{2}+ 2^{a}p^{b}= y^{n} - (with B. He, A. Pinter, N.Varga),
. Glas. Mat. Ser. III,Vol. 50 (70) (2015), 35 – 41.*A generalization of a problem of Mordell* - With M. Le, H. Zhu),
. Publicationes Mathematicae Debrecen, 2014 / 85 / 3-4 (10).*On a pure ternary Diophantine equation* - (with A. Filipin, Y. Fujita),
. Journal of Number Theory, Volume 145 (December 2014), 604-631.*The extendibility of Diophantine pairs II: Examples* - (with S. Yang),
. Journal of Number Theory, Volume 140 (July 2014), 226-234.*Proof of the P-integer conjecture of Pomerance* - (with H. Godinho, T. Porto),
. Acta Math. Hungar. 143 (1) (2014), 249–268.*On the Diophantine Equation v(v+1)=u(u+a)(u+2a)* - (with A. Filipin, Y. Fujita ),
. Glas. Mat. Ser. III, Vol. 49, No. 1 (2014), 25-36.*The extendibility of Diophantine pairs I: the general case* Afrika Mathematika. (2014) 25, 739–744.*Note on the Diophantine equation y*^{2}=px(Ax^{2}+2).- (with B. He, S. Yang, W. Wu),
.**The solution number of the Diophantine equations y**^{2}=nx(Ax^{2}C)*±**The South Pacific Journal of Pure and Applied Mathematics*, Vol. 02, No. 02, 2013, 1-13. - (with S. Yang, W. Wu),
**Diophantine equations involving normalized binomial mid-coefficients**. Publicationes Mathematicae Debrecen 2013 / 83 / 3 (11). - (with B. He, I. Pink, A. Pinter),
≤*On the Diophantine inequality |X*^{2}-cXY^{2}+Y^{4}|. Glas. Mat. Ser. III 48(68) (2013) 291-299.*c+2* - (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), 119-135. - (with D. Marques),
. Proceedings of Japan Mathematics Academy, Ser. A . Proceedings of Japan Mathematics Academy, 89 Ser. A (2013) 47-50.*Fibonacci and Lucas numbers of the form 2*^{a}+ 3^{b}+ 5^{c} - (with H. Godinho, D. Marques),
. Communications in Mathematics journal, 20 (2012) 81-88.*On the Diophantine equation x*^{2}+ 2^{α}5^{β}17^{γ}= y^{n} - (with D. Marques),
. Rendiconti dell’ Istituto di Matematica dell’ Universita’ di Trieste, Volume 44 (2012), 393-397.**On repdigits as product of consecutive Fibonacci numbers** - (with Y. Fujita),
Periodica Mathematica Hungarica, Volume 65, Issue 1, September 2012, 75-81.*The extension of the D(-k*.^{2})-pair {k^{2}, k^{2}+1} - (with T. Miyazaki),
*The Diophantine equation (2am-1)*^{x}+ (2m)^{y }=(2am+1)^{z}*.*International Journal of Number Theory, Vol. 08, No. 08, (2012) 2035-2044. - (with M. Le, H. Zhu),
. The Bulletin of the Australian Mathematical Society, Volume 86, Issue 02, October 2012, 303-314.**On the exponential Diophantine equation x**^{2}+ p^{2m }= 2y^{n} - (with D. Marques),
. Bull Braz Math Soc., New Series 43 (3), (2012) 397-406.*On the sum of powers of consecutive terms of a linear recurrence sequence* - (with A. Filipin, B. He),
. Glas. Mat. Ser. III, Vol. 47, No.1 (2012), 31-51.*On a family of two-parametric D(4)-triples* - (with B. He),
. Periodica Mathematica Hungarica Vol. 64 (1), 2012, 1-10.*On a family of Diophantine triples {k, A*s II^{2}k+2A ,(A+1)^{2}k+2(A+1)} with two parameter - (with D. Marques),
. East-West J. of Mathematics, Vol. 13, No 1 (2011) 75-79*A Diophantine equation involving C-nomial coefficients* - (with Y. Fujita),
NNTDM 17 (2011), 4, 42-49.*Uniqueness of the extension of the D(4k*^{2})-triple {k^{2}-4, k^{2}, 4k^{2}-4}. - (with A. Bajolet, B. Dupuy, F. Luca),
Publicationes Mathematicae Debrecen, 79/3-4 (2011) 269-282.*On the Diophantine equation x*.^{4}– q^{4 }= py^{r} - (with P. Yuan),
. Glas. Mat. Ser. III, Vol. 46, No.2 (2011), 325-331.*On a variant of a Diophantine equation of Cassels* - (with D. Marques),
. Colloquium Mathematicum 124 (2011), 145-155.*On terms of linear recurrence sequences with only one distinct block of digits* - (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),
Science China Mathematics 54 (2011) 1299-1316.*On the size of the intersection of two Lucas sequences of Distinct type II.* - (with K, A. Broughan, M. J. Gonzalez, R. H. Lewis, F. Luca, J. M. Huguet),
INTEGERS 11, (2011), 363-397.*There are no multiply-perfect Fibonacci numbers*. - (with S. Yang),
Annales des sciences mathématiques du Québec, 35, no. 1 (2011), 137-40.*On a conjecture of the power series coefficients of the function U(n, x).* - (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), 227-234. - (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), 31-61. - (with J. Luo, P. Yuan),
INTEGERS 11A, (2011), Article 27.*On some equations related to Ma’s conjecture.* - (with S. Yang, B. He),
Journal of Number Theory, 131, no. 10, (2011) 1840-1851.*Diophantine equations with products of consecutive values of a quadratic polynomial.* - (with B. He),
Journal of Number Theory, Volume 131, Issue 1, (2011) 120-137.*On the D(-1) triple {1, k*.^{2}+1, k^{2}+2k+2} and its unique D(1)-extension - (with D. Marques),
. Proceedings of Japan Mathematics Academy, Ser A, December 2010, 174-176.*On the sum of powers of two consecutive Fibonacci numbers* - (with S. Yang, B. He),
*A note on the Diophantine equation |a*^{x}– b^{y}| = c*.*Mathematica Scandinavica Volume 107, Number 2, (2010) 161-173. - (with B. He, M. Ulas),
**O**. The Bulletin of the Australian Mathematical Society 82 (2010) 187-204.*n the Diophantine equation z*II^{2}= f(x)^{2}± f(y)^{2} - (with B. He, P. Yuan),
. Functiones et Approximatio Commentarii Mathematici Volume 43, Number 1 (2010), 31-44.*On the Diophantine equation X*^{2 }– (p^{2m}+ 1)Y^{6 }= -p^{2m} - (with A. Filipin, B. He),
Fibonacci Quart. 48 (2010), no. 3, 219–227.*On the D(4)-triple {F*._{2k}, F_{2k+6}, 4F_{2k+4}} - (with D. Marques),
. C. R. Acad. Sci. Paris, Ser. I 348 (2010) 717–720.*Perfect Powers among Fibonomial Coefficients* - (with B. He),
. The Bulletin of the Australian Mathematical Society, (2010), 81 177-185.*On the number of solutions of the Diophantine equation ax*^{m }– by^{n}= c - (M. Ulas),
**O***n the Diophantine equation z*^{2}= f(x)^{2}± f(y)^{2}*.*Publicationes Mathematicae Debrecen 76/1-2 (2010), 183-201. - (with O. Kihel, F. Luca),
*Variants of the Diophantine Equation n! + 1 = y*^{2}*.*Portugaliae Mathematica**,**Volume 67, Issue 1 (2010), 1-11. - (with F. Luca, P. Stanica),
Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 1–8.**On a Diophantine equation of Stroeker.** - (with F. Luca),
*On the Diophantine Equation x*^{4 }– q^{4 }= py^{3}*.*Rocky Mountain Journal of Mathematics, vol. 40, no. 3, (2010) 995-1008. - (with B. He),
. Ann. Sci. Math. Québec*A remark on the generalized Ramanujan-Nagell equation x*^{2}– D = k^{n}**33**(2009), no 2, 165-169. - (with A. Filipin),
Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 25, No. 2, (2009), 145-153.*On the family of Diophantine triples {k+2, 4k, 9k+6}*. - (with B. He, B. Jadrijevic),
. Glas. Mat. Ser. III, Vol. 44 (64) (2009), 309 – 321.*Solutions of a class of quartic Thue inequalities* - (with F. Luca, S. Tengely),
. Ann. Sci. Math. Québec*On the Diophantine Equation x*^{2}+ C = 4y^{n}**33**(2009), no 2, 171-184. - (with B. He),
The Glasgow Mathematical Journal, Volume 51, Issue 03, September 2009, 659-667.*The Diophantine equation n*.^{x }+ (n+1)^{y}= (n+2)^{z}revisited - (with S. Yang, B. He),
*A 2×2 Lattice space-time code of the highest rank**.*Proceedings of the American Mathematical Society,**137**(2009), 3601-3607. *On the positive integral solutions of the Diophantine equation x*^{3 }+ by + 4 – xyz = 0*.*African Diaspora Journal of Mathematics, 8 (2009), No. 1, 81-89.- (with B. He)
Acta Mathematica Hungarica., 124 (1-2) (2009), 99-113.*On a family of Diophantine triples {k, A*^{2}k+2A ,(A+1)^{2}k+2(A+1)} with two parameters. - (with F. Luca)
Colloquium Mathematicum, 116 (2009), 139-146.*On the Diophantine equation x*^{2}+ 2^{a}13^{b}= y^{n}. - (with S. Akhtari, P. G. Walsh),
*Addendum on the equation aX*^{4 }– bY^{2}=2*.*Acta Arithmetica 137 (2009), 199-202. - (with B. He),
Periodica Mathematica Hungarica, 58 (1) (2009), 59-70.*On the family of Diophantine triples {k+1, 4k, 9k+3}.* - (with B. He, G. P. Walsh)
*On the Diophantine equation X*^{2 }– (2^{2m}+1)Y^{4}=-2^{2m}*.*Publ. Math. Debrecen, 73/3-4 (2008) 417-420. - (with B. He),
. Acta Arith.*Simultaneous Pellian equations with a single or no solution***134**(2008), 369-380. - (with B. He),
Indag. Mathem., N.S., 19 (1) (2008), 65-72.*On the number of solutions of Goormaghtigh equation for given x and y.* *On the solutions of a parametric family of cubic Thue equations**.*Bull Braz Math Soc, New Series 39 (4) (2008), 537-554.- (with F. Luca),
. Bull. Malays. Math. Sci. Soc. (2) 31 (2) (2008), 129–134.*On the positive integral solutions of the Diophantine equation x*^{3 }+ by + 1 – xyz=0 - (with F. Luca),
Int. J. Number Theory, 4, (6) (2008), 973-979.**On the Diophantine equation x**.^{2}+ 2^{a}5^{b}= y^{n} - (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), 430-442. - (with F. Luca),
. C. R. Acad. Sci. Paris, Ser. I 346 (2008) 487–489.**On binary palindromes of the form 10**^{n}± 1 - (with F. Luca),
Diophantine Equation, Editor: N. Saradha, Narosa Publishing House, (2008), pp. 135-149.**On the numbers of the form ± x**^{2 }± y! - (with S. Akhtari, P.G. Walsh),
. Acta Arith.**On the equation aX**^{4}– bY^{2}= 2**131**(2008), 145-169. - (with F. S. Abu Muriefah and F. Luca),
. The Glasgow Mathematical Journal, Volume 50, Issue 01, January 2008, pp 175-181.**On the Diophantine equation x**^{2}+ 5^{a}13^{b}= y^{n} - (with F. Luca),
. The Fibonacci Quarterly Vol. 54.4 (2007) 322-326.*On the Diophantine equation x*^{2}+ 7^{2k}= y^{n} - (with E. Goins),
. International Journal of Pure and Applied Mathematics, Volume*On Pythagorean Quadruplets***35**, No. 3 (2007), 363-372. -
. Acta Arith.*A parametric family of sextic Thue equations***125**(2006), 347-361. *A Note on the Diophantine Equation x! + A = y*^{2}II*.*International Journal of Applied Mathematics & Statistics, Vol.**6**, No. D06 (2006), 25-32.*Complete Solutions of a Family of Cubic Thue Equations**.*Journal de Theorie des Nombres de Bordeaux 18 (2006), 285-298, and 26 (2016), 287-288.- (with M. Bennett, G. P. Walsh),
International Journal of Number Theory, Vol. 2, No. 2 (June 2006) 195-206.*A generalization of a theorem of Bumby on quartic Diophantine equations*. . RJooiA, Transactions on Mathematics, Spring 2006, pp. 125-129.*A Note on the Diophantine Equation x*^{2}+ D = p^{n}. C. R. Math. Rep. Acad. Sci. Canada Vol. 28. (1), 2006 pp. 24-32.*On the solutions of a family of quartic Thue equations II*International Journal of Pure and Applied Mathematics, Volume 26, No. 4 (2006), 565-571.*A Note on the Diophantine Equation x! + A = y*^{2}.- (With P. M. Voutier, G. P. Walsh),
Acta Arithmetica 120 (2005), 39-5*Solving a family of Thue equations with an application to the equation x*^{2}– Dy^{4}= 1. - (with C. Heuberger and V. Ziegler),
. J. Symbolic Computation**Automatic solution of families of Thue equations and an example degree 8****38**(2004), Issue 3, 1145-1163. -
. J. Number Theory*A Parametric Family of Cubic Thue Equations***107**(2004), 63-79 and Journal of Number Theory, Volume 150, (May 2015) Pages 206-207. . Number Theory for the Millennial, Bruce Berndt, et. al., editors, A.K. Peters Ltd, 2002, Volume III, 285-299.*On the solutions of a family of sextic equations*. Math. Comp.*On the solutions of a family of quartic equations***69**(2000), 839-849.. Proceedings of the 11*On binary quadratic forms*^{th}Conference of ACMS, 1997, 125-135.