Alain S. Togbe, Ph. D.
 Associate Professor of Mathematics

 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


Office Hours - Spring 2009 
Monday & Wednesday

  11:30 AM - 1:00 PM

Tuesday & Thursday

   By appointment

Friday

  By appointment


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 ax+(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 nx + (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 + 2α 13β = 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 + 2a 5b = 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 – (22m +1)Y4=-22m. 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 + 2α 5β 13γ = 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 + 5a 13b = yn, Glasgow Mathematical Journal, Volume 50, Issue 01, January 2008, 175-181.

  25. (with F. Luca) On the Diophantine equation x2 + 72k = 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.

Professional Membership:
    AMS
    MAA
    CMS-SMC

    ACMS
    CAARMS

 


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Math/Statistics/Physics Department
 
Modified: May 15, 2009
atogbe@pnc.edu