Alain S.Togbe, Ph.D
 Professor of Mathematics

 Mathematics/Statistics/Physics Department
 Purdue University North Central

 1401 S. U.S. 421
 Westville, IN 46391 USA

 Phone: (219) 785-5458
 Fax: (219) 785-5772
 atogbe@pnc.edu
 Office: SWRZ 302
 

Education

  Laval University, Quebec, Canada, Ph.D. in Mathematics, 1997.

  Laval University, Quebec, Canada, MS in Mathematics, 1994.

  University of Abidjan, Ivory Coast, DEA in Mathematics, 1988.

  National University of Benin, Teaching Certificate, 1985.

  National University of Benin, BS in Mathematics, 1984.


Teaching: Spring 2014

OFFICE HOURS

Monday

1:00 - 1:50 or by appointment

Tuesday

 

Wednesday

11:00 - 11:50 or by appointment

Thursday

 

Friday

1:00 - 1:50 or by appointment

 

Research

  Algebraic Number Theory, especially Diophantine equations.

 

Conferences

CIMPA/ICTP Summer research school in Benin

Conference on Diophantine m-tuples and related problems

 

Selected PublicationsOn a pure ternary exponential Diophantine equation

  1. (With M. Le, H. Zhu), On a pure ternary Diophantine equation, Accepted to appear in Publicationes Mathematicae Debrecen.
  2. (with S. Yang), Proof of the P-integer conjecture of Pomerance, Accepted to appear in the Journal of Number Theory.
  3. (With H. Zhu, M. Le, G. Soydan), On the exponential Diophantine equation x2 + 2a pb = yn, Accepted to appear in Periodica Mathematica Hungarica.
  4. (with H. Godinho, D. Marques), On the Diophantine equation x2 + C = yn for C =2a 3b 17c and C =2a 13b 17c. Acccepted to appear in Mathematica Slovaca.
  5. (with H . Godinho, T. Porto), On the Diophantine Equation v(v+1)=u(u+a)(u+2a). Accepted to appear in Acta Mathematica Hungarica.
  6. (with A. Filipin, Y. Fujita ), The extendibility of Diophantine pairs I: the general case. Accepted to appear in Glas. Mat. Ser. III.
  7. (with B. He, S. Yang, W. Wu), The solution number of the Diophantine equations y2=nx(Ax2\pm C) . Accepted to appear in The South Pacific Journal of Pure and Applied Mathematics.
  8. (with S. Yang, W. Wu), Diophantine equations involving normalized binomial mid-coefficients. Accepted to appear in Publicationes Mathematicae Debrecen.

  9. (with B. He, I. Pink, A. Pinter) On the Diophantine inequality |X2-cXY2+Y4|<= c+2 , Accepted to appear in Glas. Mat. Ser. III.
  10. A note on the Diophantine equation y2 =px(Ax2 +2) , Accepted to appear in Afrika Mathematika.
  11. (with S. Yang, B. He), On the solutions of the exponential Diophantine equation ax+ by =(m2+1)z, Quaestiones Mathematicae, 36 (2013), 119-135.

  12. (with D. Marques), Fibonacci and Lucas numbers of the form 2a + 3b + 5c . Proceedings of Japan Mathematics Academy, Ser. A . Proceedings of Japan Mathematics Academy, 89 Ser. A (2013) 47-50.
  13. (with H. Godinho, D. Marques), On the Diophantine equation x2 + 2α 5β 17γ = yn. Communications in Mathematics journal, 20 (2012) 81-88.

  14. (with D. Marques), On repdigits as product of consecutive Fibonacci numbers. Rendiconti dell' Istituto di Matematica dell' Universita' di Trieste, Volume 44 (2012), 393-397.

  15. (with Y. Fujita), The extension of the D(-k2)-pair {k2, k2+1}. Periodica Mathematica Hungarica, Volume 65, Issue 1, September 2012, 75-81.

  16. (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.

  17. (with M. Le, H. Zhu), On the exponential Diophantine equation x2 +  p2m = 2yn. The Bulletin of the Australian Mathematical Society, Volume 86, Issue 02, October 2012, 303 - 314.

  18. (with D. Marques), On the sum of powers of consecutive terms of a linear recurrence sequence. Bull Braz Math Soc., New Series 43(3), (2012) 397-406.

  19. (with A. Filipin, B. He) On a family of two-parametric D(4)-triples. Glas. Mat. Ser. III, Vol. 47, No.1 (2012), 31-51.

  20. (with B. He) On a family of Diophantine triples {k, A2k+2A ,(A+1)2k+2(A+1)} with two parameters II.  Periodica Mathematica Hungarica Vol. 64 (1), 2012, 1-10.

  21. (with D. Marques), A Diophantine equation involving C-nomial coefficients. East-West J. of Mathematics, Vol. 13, No 1 (2011) 75-79

  22. (with Y. Fujita), Uniqueness of the extension of the D(4k2)-triple {k2-4, k2, 4k2-4}. NNTDM 17 (2011), 4, 42–49.

  23. (with A. Bajolet, B. Dupuy, F. Luca), On the Diophantine equation x4 - q4 = pyr. Publicationes Mathematicae Debrecen, 79/3-4 (2011) 269-282.  

  24. (with P. Yuan), On a variant of a Diophantine equation of Cassels. Glas. Mat. Ser. III, Vol. 46, No.2 (2011), 325-331.

  25. (with D. Marques), On terms of linear recurrence sequences with only one distinct block of digits. Colloquium Mathematicum 124 (2011), 145-155.

  26. (with B. He, O. Kihel), Solutions of a class of quartic Thue inequalities. Computers and Mathematics with Applications 61 (2011) 2914–2923.

  27. (with M. Cipu, M. Mignotte), On the size of the intersection of two Lucas sequences of Distinct type II. Science China Mathematics 54 (2011) 1299-1316.

  28. (with K, A. Broughan, M. J. Gonzalez, R. H. Lewis, F. Luca, J. M. Huguet) There are no multiply-perfect Fibonacci numbers.  INTEGERS 11, (2011), 363-397.

  29. (with S. Yang),  On a conjecture of the power series coefficients of the function U(n, x). Annales des sciences mathématiques du Québec, 35, no. 1 (2011), 137-40.

  30. (with B. He) On the positive integer solutions of the exponential Diophantine equation ax+(3a2-1)y=(4a2-1)z. Advances in Mathematics (Chinese) Vol. 40, No. 2, (2011), 227-234.

  31. (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.

  32. (with J. Luo, P. Yuan), On some equations related to Ma's conjecture. INTEGERS 11A, (2011), Article 27.

  33. (with S. Yang, B. He), Diophantine equations with products of consecutive values of a quadratic polynomial., Journal of Number Theory, 131, no. 10, (2011) 1840-1851.

  34. (with B. He) On the D(-1) triple {1, k2+1, k2+2k+2} and its unique D(1)-extension. Journal of Number Theory,   Volume 131, Issue 1, (2011) 120-137.

  35. (with D. Marques), On the sum of powers of two consecutive Fibonacci numbers, Proceedings of Japan Mathematics Academy, Ser A, December 2010, 174-176.

  36. (with S. Yang, B. He), A note on the Diophantine equation |ax - by|=c. Mathematica Scandinavica Volume 107, Number 2, (2010) 161-173.

  37. (with B. He, M. Ulas) On the Diophantine equation z2 = f(x)2 ± f(y)2 II. The Bulletin of the Australian Mathematical Society 82 (2010) 187-204.

  38. (with B. He, P. Yuan) On the Diophantine equation X2 - (p2m + 1)Y6 = -p2m. Functiones et Approximatio Commentarii Mathematici Volume 43, Number 1 (2010), 31-44.

  39. (with A. Filipin, B. He) On the D(4)-triple {F2k, F2k+6, 4F2k+4}.  Fibonacci Quart. 48 (2010), no. 3, 219–227.

  40. (with D. Marques) Perfect Powers among Fibonomial Coefficients. C. R. Acad. Sci. Paris, Ser. I 348 (2010) 717–720.

  41. (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.

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

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

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

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

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

  47. (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.

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

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

  50. (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.

  51. (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.

  52. 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.

  53. (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.

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

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

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

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

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

  59. (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.

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

  61. (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.

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

  63. (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.

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

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

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

  67. (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.

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

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

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

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

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

  73. (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.

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

  75. 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.

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

  77. (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

  78. (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.

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

  80. 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.

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

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

 


Membership

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PNC
Mathematics/Statistics/Physics Department