Algebraic Number Theory, Elliptic Curves, Diophantine Equations. Permutation polynomials over Finite Fields, Galois Theory, and Cryptography.

The 25^th Annual Meeting in Mathematics (AMM 2021), Bangkok, Thailand: Keynote speaker

Amicale de théorie des nombres en hommage à Robert Langlands, Canadian Mathematical Society, 7-11 June 2021: Invited to give a talk

Polynomials and Arithmetic, Lille, France, postponed, hopefully to 2021: Invited to give a talk

The Third International Conference on Pure and Applied Mathematics (ICPAM3), Papua New Guinea, postponed: Invited talk

Leuca2022, May 16-21, 2022, Marina di San Gregorio, Patù (Lecce), Italy: Invited talk

The Mathematical Congress of the Americas 2021, July 19 to 23, session of ‘NUMBER THEORY IN THE AMERICAS’, invited to give a talk

Teaching award in the faculty of Mathematics and Statistics, Excellence in teaching, Brock University, June 2017.

Fellow of the Papua New Guinea Mathematical Society since November 2013

Publications (since 2010) in referred journals

1. (With S. Kebli, J. Larone and F. Luca), On the nonnegative integer solutions to the equation Fn ± Fm = y^a, J. Number Theory, 220, 107-227 (2021).
2. On the nonnegative integer solutions to the equation Fn + Fm = y^a, accepted for publication by Quaestiones Mathematicae, 2020.
3. (With Boumahdi, Larone and Yadjel), A new proof of the Carlitz-Lutz theorem, Bull. Aust. Math. Soc. 101, No. 1., 56-60, (2020),
4. (With M. Ayad and R. Bouchenna), Indices in a Number Field II, Int. J. Number Theory, 15, No. 1., 89-103, (2019).
5. (With N. Berbara, M. Sukrawan and J. Midgley), On the Diophantine Equation h(a)x² +f(a) = g(a)aⁿ, Funct. Approximatio. Comment. Math. 61. No. 2. 201-206, (2019).
6. (With R. Boumahdi and M. Sukrawan), Proof of the Conjecture of Keskin, Siar and Karaatli, Annales Academia Scientiarum Fennica Mathematica, Vol 43, 2018, 1–5.
7. (With T. Garici and J. Larone), The number of solutions to y²=px( Ax² +2), Publications de l’Institut Mathematique . 2018, Vol. 104, Issue 118, 149-156, (2018).
8. (With M. Ayad and R. Bouchenna), Indices in a Number Field, Journal Theorie des Nombres de Bordeaux,29, No 1., 201-216. (2017)
9. (With N. Benyahia Tani and Sadek Bouroubi), An effective approach for integer partitions using exactly two distinct sizes of parts, Elemente der Mathematik, 72, No. 2., 66-74, (2017).
10. (With F. Bencherif, N. Benyahia Tani and Sadek Bouroubi), Integer Partitions into Diophantine Pairs, Quaestiones Mathematicae, 40, No. 4., 435-442, (2017).
11. (With M. Ayad and J. Larone), When does a given polynomial with integer coefficients divide another? The American Mathematical Monthly, 123(04): 376-381, (2016).
12. (With S. Kebli) On a variant of Lucas’ square pyramid problem. Ann. Math. Inf, Volume 46, 245-250, 2016.
13. (With M. Ayad and A. Bayad), On the denominator of an algebraic number in a number field, J. Number Theory 149, 1-14 (2015).
14. (With Jesse Larone), Prime rational functions, Acta Arith. 169, No. 1, 29-46 (2015).
15. (With M. Ayad and K. Belghaba), On Permutation Binomials over Finite Fields, The Rocky Mountain Journal of Mathematics, 45, No. 2, 389-399 (2015).
16. (With M. Ayad and K. Belghaba), On Permutation Binomials over Finite Fields, The Bulletin of The Australian Mathematical Society, Volume 89, Issue 01, 112-124, 2014.
17. (With M. Ayad and V. Coia), On relatively prime sets, J. Integer Sequences, 17, No. 3, Article 14.3.7, 8 p, 2014.
18. (With M. Ayad), A new class of permutation polynomials of F_q, Elemente der Mathematik, volume 68, n 2, 53-55, 2013.
19. (With M. Talbi and J. Van Druten A parametric family of dihedral extensions of degree 12 over Q and an independent system of units Ann. Sci. Math. Québec 36 (2012), 2, 535-543
20. (With Lizotte), Small generators and reduced elements in a quadratic number field, J. Number Theory, Volume 132, Issue 9, September 2012, 1888–1895.
21. (With Ayad), Recognizing the primes using permutations, Inter. J. Number Theory, Vol. 8, No. 8 (2012) 2045–2057.
22. (With B. He and A. Togbe) Solutions of a class of quartic Thue inequalities, Computers & Mathematics with Applications Volume 61, (2011), 2914-2923.
23. (With Ayad), Common Divisors of Values of Polynomials and Common Factors of Indices in a Number Field, accepted for for publication, Inter. J. Number Theory, Volume: 7, Issue: 5 (2011), 1173-1194.
24. (With Luca and A. Togbe), VARIANTS OF THE DIOPHANTINE EQUATION n! + 1 = y², Portugal. Math. (N.S.) Portugaliae Mathematica, Vol. 67, Fasc. 1, 2010, 1–11.