Alain Togbe, Ph. D.
Professor of Mathematics

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

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

Education
Ph.D. in Mathematics (Number Theory), Laval University, Quebec, Canada, 1997.
M.S. in Mathematics (Number Theory), Laval University, Quebec, Canada, 1994.

DEA in Mathematics (Differential Geometry), University of Abidjan, 1988.
 B.S. in Mathematics, National University of Benin, 1984.

 

Teaching: On sabbatical leave

OFFICE HOURS

 

Monday

 

Tuesday

 

Wednesday

 

Thursday

 

Friday

 
 

The 2010 Fall MAA Indiana Section meeting will be held at PNC.

For any questions, please email me. Thanks

Courses Taught :   Please go to Blackboard


   

Research

Algebraic Number Theory, specially Diophantine equations

 

Selected Publications

  1. (with D. Marques) Perfect Powers among Fibonomial Coefficients. Accepted to appear in C. R. Acad. Sci. Paris.

  2. (with B. He, P. Yuan) On the Diophantine equation X2 - (p2m + 1)Y6 = -p2m. Accepted to appear in Functiones et Approximatio Commentarii Mathematici.

  3. (with B. He, M. Ulas) On the Diophantine equation z2 = f(x)2 ± f(y)2 II. Accepted to appear in The Bulletin of the Australian Mathematical Society.

  4. (with K, A. Broughan, M. J. Gonzalez, R. H. Lewis, F. Luca, J. M. Huguet) There are no multiply-perfect Fibonacci numbers.  Accepted to appear in Integers.

  5. (with B. He) On a family of Diophantine triples {k, A2k+2A ,(A+1)2k+2(A+1)} with two parameters II.  Accepted to appear in Periodica Mathematica Hungarica.

  6. (with S. Yang, B. He),  A note on the Diophantine equation |ax - by|=c. Accepted to appear in Mathematica Scandinavica.

  7. (with S. Yang),  On a conjecture of the power series coefficients of the function U(n, x). Accepted to appear in Annales des sciences mathématiques du Québec.

  8. (with A. Filipin, B. He) On the D(4)-triple {F2k, F2k+6, 4F2k+4}.  Accepted to appear in The Fibonacci Quarterly.

  9. (with B. He, P. G. Walsh) On the size of the intersection of two Lucas sequences of distinct type. Accepted to appear in Annales des sciences mathématiques du Québec.

  10. (with B. He) On the positive integer solutions of the exponential Diophantine equation ax+(3a2-1)y=(4a2-1)z. Accepted to appear in Advances in Mathematics (Chinese).

  11. (with B. He) On the D(-1) triple {1, k2+1, k2+2k+2} and its unique D(1)-extension.

  12. (with F. Luca) On the Diophantine Equation x4 - q4 = py3. Rocky Mountain Journal of Mathematics, vol. 40, no. 3, (2010)  995-1008.

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

  14. (with B. He) On the number of solutions of the Diophantine equation axm - byn = c. The Bulletin of the Australian Mathematical Society, (2010), 81 177-185.

  15. (with O. Kihel, F. Luca) Variants of the Diophantine Equation n! + 1 = y2. Portugaliae Mathematica, Volume 67, Issue 1 (2010), 1-11.

  16. (with M. Ulas) On the Diophantine equation z2 = f(x)2 ± f(y)2. Publicationes Mathematicae Debrecen  76/1-2 (2010), 183-201.

  17. (with F. Luca, S. Tengely) On the Diophantine Equation x2 + C = 4yn. Ann. Sci. Math. Québec 33 (2009), no 2, 171-184.

  18. (with B. He) A remark on the generalized Ramanujan-Nagell equation x2 - D = kn. Ann. Sci. Math. Québec 33 (2009), no 2, 165-169.

  19. (with A. Filipin) On the family of Diophantine triples {k+2, 4k, 9k+6}. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis,  Vol. 25, No. 2, (2009), 145-153.

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

  21. (with B. He) The Diophantine equation nx + (n+1)y = (n+2)z revisited. The Glasgow Mathematical Journal, Volume 51, Issue 03, September 2009, 659-667.

  22. (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.

  23. On the positive integral solutions of the Diophantine equation x3 + by + 4 – xyz = 0. African Diaspora Journal of Mathematics, 8 (2009), No. 1, 81-89.

  24. (with B. He) On a family of Diophantine triples {k, A2k+2A ,(A+1)2k+2(A+1)} with two parameters. Acta Mathematica Hungarica., 124 (1-2) (2009), 99-113.

  25. (with F. Luca) On the Diophantine equation x2 + 2a 13b = yn. Colloquium Mathematicum, 116 (2009), 139-146.

  26. (with S. Akhtari,  P. G. Walsh) Addendum on the equation aX4 - bY2=2. Acta Arithmetica 137 (2009), 199-202.

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

  28. (with Bo He, G. P. Walsh) On the Diophantine equation X2 – (22m +1)Y4=-22m. Publ. Math. Debrecen, 73/3-4 (2008) 417-420.

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

  30. (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.

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

  32. (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.

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

  34. (with E. Goins and 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.

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

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

  37. (With S. Akhtari, P.G. Walsh) On the equation aX4 - bY2 = 2.. Acta Arith. 131 (2008), 145-169.

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

  39. (With F. Luca) On the Diophantine equation x2 + 72k = yn.  The Fibonacci Quarterly Vol. 54.4 (2007) 322-326.

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

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

  42. A Note on the Diophantine Equation x! + A = y2II. International Journal of Applied Mathematics & Statistics, Vol. 6, No. D06 (2006), 25-32.

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

  44. (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) 195-206.

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

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

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

  48. (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), 39-5

  49. (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, 1145-1163.

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

  51. 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, 285-299.

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

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

Membership:

AMS

MAA

CMS

ACMS
 


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