Purdue University North Central
 1401 S. U.S. 421
 Westville, IN 46391 USA

 Phone: (219) 785-5458
 Fax: (219) 785-5507
 atogbe@pnc.edu
 Office: SWRZ 302

Education
     Ph.D., Algebraic Number Theory, Laval University, Quebec, Canada, 1997
     M.S., Algebraic Number Theory, Laval University, Quebec, Canada, 1994

     DEA, Differential Geometry, University of Abidjan, Ivory Coast, 1988.
     B.S., Mathematics, National University of Benin, Abomey-Calavi, Benin, 1984

Courses Spring 2009:
    Go to Blackboard for any information related to your class.

Research Interests:
    Diophantine equations, especially Thue equations

Publications:

1. (with Alan Filipin) On the family of Diophantine triples {k+2,4k,9k+6}. Accepted.

2. (with B. He) On the positive integer solutions of the exponential Diophantine equation a^x+(3a²-1)^y=(4a²-1)^z. Submitted.

3. (with S. Yang, B. He) A 2×2 Lattice space-time code of the highest rank. Accepted.

4. (with O. Kihel, F. Luca) Variants of the Diophantine Equation n! + 1 = y². Accepted.

5. (with B. He, B. Jadrijevic) Solutions of a class of quartic Thue inequalities. Accepted.

6. (with B. He) On a family of Diophantine triples {k, A²k+2A ,(A+1)²k+2(A+1)} with two parameters. Accepted.

7. (with B. He) The Diophantine equation n^x + (n+1)^y = (n+2)^z revisited. Accepted.

8. (with F. Luca, P. Stanica) On a Diophantine equation of Stroeker. Accepted.

9. (with F. Luca) On the Diophantine Equation x⁴ - q⁴ = py³. Accepted.
10. On the Positive Solutions of the Diophantine Equation x³ + by+4-xyz=0. Afr. Diaspora J. Math. 8(2009), No. 1, 81-89.
11. (with F. Luca) On the Diophantine equation x² + 2^α 13^β = yⁿ. Colloq. Math. 116 (2009), 139-146.
12. (with S. Akhtari,  P. G. Walsh) Addendum on the equation aX⁴ - bY²=2. Acta Arith. 137 (2009), 199-202.

13. (with B. He) On the family of Diophantine triples {k+1, 4k, 9k+3}. Periodica Mathematica Hungarica 58 (1), 2009, 59-70.

14. (with F. Luca) On the Diophantine equation x² + 2^a 5^b = yⁿ. Int. J. Number Theory, 4, (6) (2008), 973-979.

15. On the solutions of a parametric family of cubic Thue equations. Bull Braz Math Soc, New Series 39 (4) (2008), 537-554.

16. (with B. He) On the number of solutions of Goormaghtigh equation for given x and y. Indag. Mathem., N.S., 19 (1) (2008), 65-72.

17. (with B. He, G. P. Walsh) On the Diophantine equation X² – (2^2m +1)Y⁴=-2^2m. Publ. Math. Debrecen, 73/3-4 (2008) 417-420.

18. (with F. Luca) On the positive integral solutions of the Diophantine equation x³ + by + 1 - xyz=0. Bull. Malays. Math. Sci. Soc. (2) 31 (2) (2008), 129–134.

19. (with B. He) Simultaneous Pellian equations with a single or no solution, Acta Arith. 134 (2008), 369-380.

20. (with E. Goins, F. Luca) On the Diophantine Equation x² + 2^α 5^β 13^γ = yⁿ. ANTS VIII Proceedings: A.J. van der Poorten and A. Stein (eds.), ANTS VIII, Lecture Notes in Computer Science 5011 (2008), 430-442.

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

22. (with F. Luca) On the numbers of the form ± x² ± y!. Diophantine Equation, Editor: N. Saradha, Narosa Publishing House, (2008), 135-149.

23. (with S. Akhtari,  P. G. Walsh) The Diophantine equation aX⁴ - bY²=2. Acta Arith. 131 (2008), 145-169.

24. (with F. S. Abu Muriefah,  F. Luca) On the Diophantine equation x² + 5^a 13^b = yⁿ, Glasgow Mathematical Journal, Volume 50, Issue 01, January 2008, 175-181.

25. (with F. Luca) On the Diophantine equation x² + 7^2k = yⁿ. The Fibonacci Quarterly, Vol. 54.4 (2007) 322-326.

26. (with E. Goins) On Pythagorean Quadruplets. International Journal of Pure and Applied Mathematics, Volume 35, No. 3 (2007), 363-372.

27. A parametric family of sextic Thue equations. Acta Arith. 125 (2006), 347-361.

28. A Note on the Diophantine Equation x! + A = y², II. International Journal of Applied Mathematics & Statistics, Vol. 6, No. D06 (2006), 25-32.

29. Complete Solutions of a Family of Cubic Thue Equations, Journal de Theorie des Nombres de Bordeaux 18 (2006), 285-298. 

30. (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 (2006) 195-206.

31. A Note on the Diophantine Equation x² + D = pⁿ , RJooiA, Transactions on Mathematics, Spring 2006, 125-129.

32. On the solutions of a family of quartic Thue equations II, C. R. Math. Rep. Acad. Sci. Canada Vol. 28. (1), (2006), 24-32.

33. A Note on the Diophantine Equation x! + A = y². International Journal of Pure and Applied Mathematics, Volume 26, No. 4 (2006), 565-571.

34. (with P. M. Voutier, G. P. Walsh) Solving a family of Thue equations with an application to the equation x² – Dy⁴ = 1. Acta Arithmetica 120 (2005), 39-58.

35. (with C. Heuberger and V. Ziegler) Automatic solution of families of Thue equations and an example degree 8, Journal of Symbolic Computation 38 (2004), Issue 3, 1145-1163.

36. A Parametric Family of Cubic Thue Equations, Journal Number Theory 107 (2004), 63-79.

37. On the solutions of a family of sextic Thue equations, Number Theory for the Millennial, Bruce Berndt, et. al., editors, A.K. Peters Ltd, (2002), Volume III, 285-299.

38. On the solutions of a family of quartic Thue equations, Math. Comp. 69 (2000), 839-849.

39. On binary quadratic forms, Proceedings of the 11th Conference of ACMS, 1997, 125-135.