Number Theory

1. 27

Post Graduate Level

:

1. Analytic Number Theory 2. Number Theory and Foundation of Cryptography 3. Graph Theory 4. Algrebra-1 5. Algebra-II

1. Number Theory

Ph.D. Candidates	:	03
M.Tech./M.Phil. Candidates	:	11

1. Life Members of
2. Indian Mathematical Society
3. Orissa mathematical Society

1. Minor Research Project (MRP) sponsored by University Grant Commission (UGC), Completed in 2010..

International Publications

2023
1. - K. Bhoi, P. K. Ray, On the Diophantine equation Bn1 +Bn2 = 2a1 +2a2 +2a3 , Communications in Mathematics, 31, 375-392 (2023).
2. - P. K. Ray, Certain identities involving k-balancing and k- Lucas balancing numbers via matrices, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 34, 120-130 (2023).
3. - M. Behera, P. K. Ray, Multiplicative dependence between Padovan and Perrin numbers, Boletin de la Sociedad Matematica Mexicana, 29, 1-12 (2023).
2022
4. A. Behera, P. K. Ray, On the properties of balancing and Lucas-balancing p-numbers, Iran. J. Math. Sci. Inform., 17, 147-163 (2022).
5. - K. Bhoi, P. K. Ray, On the Diophantine equation Nn = xa xb + 1, Fibonacci Quarterly 60, 316-323 (2022).
6. - M. Behera, P. K. Ray, On Z dependency of algebraic integers satisfying cubic and quartic polynomials, Lithuanian Mathematical Journal, 62, 304-307 (2022).
7. - K. Bhoi, P. K. Ray, Fermat numbers in Narayana’s cows sequence, Integers, 22, #A16, 1-7 (2022).
8. - U. K. Dutta, P. K. Ray, Euler-Zagier multiple L-functions involving balancing-like polynomials associated to Dirichlet charecters, Palestine journal of mathematics, 11(2), 274-289 (2022).
9. - K. Bhoi, P. K. Ray, On the x-coordinates of Pell equations which are Narayana numbers, Integers, 22, #A107, 1-13 (2022).
10. - K. Bhoi, P. K. Ray, Narayana numbers as sums of two base b repdigits, Acta et Commentationes Universitatis Tartuensis de Mathematica, 26, 183-192 (2022).
2021
11. A. Behera, P. K. Ray, A common generalization of convolved (u, v)-Lucas first and second kinds p-polynomials, Acta Univ. Sapientiae Math., 13(2), 305-320 (2021).
12. B. K. Patel, P. K. Ray, On Balancing and Lucas-Balancing Quarternions, Communications in Mathematics, 1-17 ( 2021).
13. K. Bhoi, P. K. Ray, Perrin numbers expressible as sums of two base b repdigits, Rend. Istit. Mat. Univ. Trieste, 53, Art. No. 18, pp. 1-11 (2021).
14. K. Bhoi, P. K. Ray, Repdigits as difference of two Fibonacci or Lucas numbers, Matematychni Studii, 56(2), 124-132 (2021).
2020
15. P. K. Ray, A Cryptography method based on hyperbolic balancing and Lucas-balancing func- tions, Proyecciones journal of mathematics,39 (1), 2020, 135-152.
16. A Behera and P. K. Ray,Determinantal and permanental representations of convolved (U, V )- Lucas first kind P - polynomials, AIMS Mathematics, 5(3),2020, 1843-1855.
17. U. K. Dutta and P. K. Ray, Analytic properties of the Apostol-Vu multiple Fibonacci zeta functions, Discussiones Mathematicae-General Algebra and Applications, 40, 2020, 37-48.
18. P. K. Ray and U. K. Dutta, Analytic continuation of Apostol-Vu multiple balancing zeta functions, Integers, 20A, 2020, #A12.
19. N. Irmak, P.K. Ray, The order of appearance of the product of two Fibonacci and Lucas numbers, Acta Mathematica Hungarica, 162, 527-538 (2020).
20. U.K. Dutta, P.K. Ray On the partial finite alternating sums of reciprocals of Balancing and Lucas-Balancing numbers,Discussiones Mathematicae-General Algebra and Applications 40(2), 201-216(2020).
21. T. Komatsu, B.K.Patel, P.K. Ray, On the periodicity of Lucas-balancing Numbers and p-adic order of Balancing numbers, Iran J. Scin.Technol. Trans. Sci. 44, 557-562(2020).
2019
22. - B. K. Patel, and P.K. Ray, On the properties of (p, q) Fibonacci and (p, q) Lucas quaternions, Mathematical Reports, 21(1), 2019, 1-10.
23. U. K. Dutta, B. K. Patel and P. K. Ray, Balancing non-Wieferich primes in arithmetic progres- sions, Proceedings: Mathematical Sciences, 2019.
24. P. K. Ray, Identities concerning k-balancing and k-Lucas-balancing numbers of arithmetic indexes, AIMS Mathematics, 4(2), 2019, 308-315.
25. U. K. Dutta and P. K. Ray, On arithmetic functions of balancing and Lucas-balancing numbers, Mathematical Communications, 24, 2019, 77-81.
26. P. K. Ray, Analytic properties of Euler-Zagier multiple Lucas-balancing zeta functions, Trans. Natl. Acad. Sci. Azerb. Ser. Phys. Tech. Math. Sci., 39(1), 2019, 38-53.
27. U. K. Dutta and P. K. Ray, On the finite reciprocal sums of Fibonacci and Lucas polynomials, AIMS Mathematics, 4(6), 2019, 1569-1581.
2018
28. B.K. Patel, N. Irmak and P.K. Ray, Incomplete balancing and Lucas-balancing Numbers, To be appeared in Mathematical Reports, 20 (1) 2018.
29. U.K Dutta, B.K. Patel and P.K. Ray, A brief remark on balancing Wieferich primes, Mathe- matica, 60 (3), 2018.
30. B K Patel, S K Sunanda and P K Ray, The period of balancing numbers modulo product of consecutive Lucas-balancing numbers, Mathematica, 60 (83), 2018, 181-185.
31. B. K. Patel, P.K. Ray and M Sahukar, Positive integers solutions of certain Diophantine equations, Proceedings: Mathematical Sciences, 128(1), 2018, 1-9.
32. D. Behera, U K Dutta and P K Ray, On Lucas-balancing zeta function, Acta et Commentationes Universitatis Tartuensis de Mathematica, 22(1), 2018, 65-74.
33. U K Dutta, P K Ray and S S Pradhan, Regularized product of balancing and Lucas-balancing numbers, Indian Journal of Mathematics, 60 (2), 2018, 171-179.
34. P. K. Ray, N. Irmak and B. K. Patel, The rank of apparition of powers of Lucas sequence, Turkish Journal of Mathematics, 42, 2018, 1566-1570.
35. T Komatsu, B.K. Patel and P.K. Ray, Higher order identities for second order sequences, An. Stint. Univ. AI. I. Cuza Lasi Mat. (N.S), LXIV, f.2, 2018, 357-368.
2017
36. P.K. Ray, On the properties of k-balancing and k-Lucas balancing numbers, Acta et Commen- tationes Universitatis Tartuensis de Mathematica,, 21, 2017.
37. P.K. Ray and S S Pradhan, Greatest common divisors for shifted balancing numbers, Boletim da Sociedade Paranaense de Mathmatica, 35, 2017.
38. P.K. Ray, Balancing polynomials and their derivatives, Ukrainian Mathematical Journal, 69 (4), 2017.
39. B.K. Patel, U.K Dutta and P.K. Ray, Period of balancing sequence modulo powers of balancing and Pell numbers, Annales Mathematicae et Informaticae, 47 (3), 2017.
2016
40. P.K. Ray, On the properties of k-balancing numbers, Article in press, Ains Shaam Engineering Journal, 2016.
41. S.M. Zahid and P. K. Ray, On closure properties of irrational and transcendental numbers under addition and multiplication, American Journal of Under Graduate Research, 13(3), 2016.
42. P.K. Ray and Juli Sahu, Generating functions for certain balancing and Lucas-balancing numbers, Palestine Journal of Mathematics, 5(2), 2016.
43. S. Swain, C. Pratihary and P.K. Ray, Balancing and Lucas-balancing numbers and their appli- cation to cryptography, Computer Engineering and Application Journal, 5(1), 2016.
44. B. K. Patel and P.K. Ray, Uniform distribution of balancing numbers modulo m, Uniform Distribution Theory, 11 (1), 2016.
45. P.K. Ray, Certain diophantine equations involving balancing and Lucas-balancing numbers, Acta et Commentationes Universitatis Tartuensis de Mathematica,, 20, 2016.
46. P.K. Ray and B. K. Patel, The period, rank and order of the sequence of balancing numbers modulo m, Mathematical Reports, 18 (3), 2016.
2015
47. P.K. Ray, Balancing and Lucas-balancing sums by matrix methods, Mathematical Reports, 17(2), 2015, 225-233.
48. P.K. Ray and S. Swain, On the Hadamard product of balancing Qn matrix and balancing Q?n matrix, TWMS journal of applied and engineering mathematics, 5(2), 2015.
49. S.M. Zahid and P. K. Ray, Approximation of Euler number using gamma function, American Journal of Under Graduate Research, 12(3), 2015.
50. P. K. Ray and G..K. Panda, Tridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers, Notes on Number Theory and Discrete Mathematics, 21(3), 2015.
2014
51. P. K. Ray, Some congruences for balancing and Lucas-balancing numbers and their applications, INTEGERS, 14, 2014, #A8.
52. P. K. Ray, Balancing sequence of matrices with application to algebra of balancing numbers, Notes on Number Theory and Discrete Mathematics, 20(1), 2014, 49-58.
53. P. K. Ray and K. Parida, Generalization of Cassini formula for balancing and Lucas-balancing numbers, Matematychni Studii, 42(1), 2014, 9-14.
2013
54. P. K. Ray, Factorization of negatively subscripted balancing and Lucas-balancing numbers, Boletim da Sociedade Paranaense de Matemática,31 (2), 2013, 161-173.
55. P. K. Ray, New identities for the common factors of balancing and Lucas-balancing numbers, International Journal of Pure and Applied Mathematics, 85(3), 2013, 487-494.
2012
56. P. K. Ray, Application of Chybeshev polynomials in factorization of balancing and Lucas- balancing numbers, Boletim da Sociedade Paranaense de Matemática, 30 (2), 2012, 49-56.
57. P. K. Ray, Curious congruences for balancing numbers, International Journal of Mathematics and Mathematical Sciences, 7 (18), 2012, 881-889.
58. P. K. Ray, Certain matrices associated with balancing and Lucas-balancing numbers, Matem- atika, 28 (1), 2012, 15-22.
2011
59. G. K. Panda and P. K. Ray, Some links of balancing and cobalancing numbers with Pell and associated Pell numbers, Bulletin of the Institute of Mathematics, Academia Sinica (New Series), 6(1), 2011, 41-72.

National Publications

2010
1. G.K. Panda and P. K. Ray, Some important properties of balancing and related number se- quences, Journal of the Orissa Mathematical Society, 29(2) (2010), 27-38.

International Conferences

1. Attended and presented the paper ‘’Diophantine equations involving balancing and their related sequences” in the international conference ‘’THUE 150” held in Institut de Mathématiques de Bordeaux, Université Bordeaux 1, France from September 30 to October 4, 2013, Sponsored by DST, India
2. Attended and presented the paper ‘’Application of some recurrence relations to cryptography using finite state machine” in the international conference ‘’ICCEIT’14” organized by ISAET held in Thailand from December 16-17, 2014. Sponsored by Conference Organizers
3. • Attended and presented the paper ‘’Certain Diophantine equations involving balancing and Lucas-balancing numbers” in the international conference ‘’DART 2016” organized by school of Mathematics and Statistics, Wuhan University, China from December 10-13, 2016. Sponsored by Conference Organizors.
4. Attended and presented the paper ‘’Abrief remark on balancing Wieferich primes” in the inter- national conference ‘’Number Theory Down Under-5” organized by Department of Mathematics, La Trobe University, Bendigo, Australia from 29-9-2017 to 2-10-2017, Sponsored by DST, India
5. Attended and presented the paper ‘’On balancing non-Wieferich primes” in the international conference ‘’Integers Conference-2018” organized by Department of Mathematics, Augusta Uni- versity, Augusta, Georgia, USA from 03-10-2018 to 06-10-2018, Sponsored by Science and Tech- nology Department, Odisha and Conference Organizors
6. Attended Mason-V mid Atlantic seminar on numbers(Online), 27-3-2021 to 28-3-2021.
7. Attended Number Theory and Representation (Online), 14-12-2020 to 18-12-2020, Valparaiso (NTRV).
8. Attended 19th Fibonacci Conference (Online),4-5-2020 to 7-5-2020
9. • Attended and presented the paper entitled "Analytic continuous of Euler-Zagier multiple bal- ancing zeta function" in International E-Conference on Pure and Applied Mathematical Sciences (ICPAMS-2022) (Online),04-05-2022 to 07-05-2022, Tunisia, Saudi Arabia.
10. Attended and presented the paper entitled Narayana numbers which are concatenations of two base b repdigits" in Integers Conference-2023, 17-05-2023 to 20-05-2023, University of Gerogia, Gerogia, Athens, USA. Sponsored by Sambalpur University and the conference Organizers

National Conferences

1. Attended and presented a paper entitled "A trigonometric approach to balancing numbers and its related sequences" in the 12th conference of the International Academy of Physical Sciences (CONIAPS XII) held in Rajasthan University, Jaipur, Rajasthan from December 22-24, 2010.
2. Attended in Pan Asian Number Theory conference (PANT 2012) held in Indian Institute of Science Education and Research(IISER), Pune from July 23-27, 2012.
3. • Attended and presented a paper entitled "New identities for the common factors of both balancing and Lucas-balancing numbers" in the international conference "The Legacy of Srinivasa Ramanujan" held in University of Delhi, New Delhi from December 17-22, 2012.
4. Attended and presented a paper “On the Hadamard product of balancing Qn matrix and balancing Q?n matrix“ in the Instructional Workshop in Applied Mathematics held at South Assian University, New Delhi during May 6-10, 2013.
5. Attended and presented the paper ‘’ Certain Diophantine equations involving balancing and their related numbers” in the international conference ‘’MSAST 2014” organized by IMBIC, Sweden, held in Kolkata, India from December 21-23, 2014.
6. Attended in the international conference ‘’Automorphic forms on metaplectic groups and related topics” organized by Boston College USA and IISER, Pune from July 4-9, 2016.
7. Attended in the international conference ‘’International Conference on Class Groups of Num- ber Fields and Related Topics-2017 (ICCGNFRT-2017 ” organized by Harish Chanda Research Institute, Allahabad from September 4-7, 2017.

Workshops

1. Attended the Instructional Workshop on Applied Mathematics for University/College teachers organized under the auspices of the centre of advanced study in applied mathematics (SAP- UGC), Kolkata University in academic collaboration with North Bengal University, Darjeeling during 24th February to 4th march, 1997 at North Bengal University, West Bengal.

Nil

1. Seminars/Conferences/ Workshops organized as a Convener
2. Organized an One day International webinar on Recurrent Sequences and Special Functions-
3. 2021 (IWRSSF-2021), Dept. Of Mathematics, Sambalpur University, Burla, 24th Feb 2021.
4. Organized a Webinar on Number Theory and Its Related Topics-2020 (Web-NTIRT-2020),
5. Dept. Of Mathematics, Sambalpur University, Burla, 06-15 July 2020.
6. Organized a National seminar on Graph Theory and its Applications (NSGTA-2020),
7. Dept. of Mathematics, Sambalpur University, Burla, 27-28 February 2020.

1. Dean Faculty, Science & Technology
2. First Appellate Authority of Sambalpur University
3. Nodal Officer Sambalpur University, SAMARTH Project
4. Library in Charge, Department of Mathematics, Sambalpur University

Present Address :  Department of Mathematics Sambalpur University , Jyoti Vihar Burla, India

Permanent Address :  Qrs No AL 56, Basanti Nagar , Rourkela-769012 Odisha, India