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राष्ट्रीय प्रौद्योगिकी संस्थान राउरकेला
National Institute of Technology Rourkela
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Team1

 Academic Identity

Orcid Id
Scopus Id
14830333100
Researcher Id
Google Scholar Id

Gopal Krishna Panda

Professor

Mathematics

 (+91) 661 246 2705 , 3705

 gkpanda[at]nitrkl.ac.in

 Biosketch

44

Publications       

0

Sponsored Projects

0

Consultancy Projects

14

Doctoral Students

0

Continuing Education

10

PG Dissertation

 Personal Information

Prof. Gopal Krishna Panda

Professor

Mathematics

Joined in Feb 1989

 Room Number: MN-324

 Department of Mathematics, National Institute of Technology Rourkela, Sundargarh, Odisha, India - 769008

 Education Qualification

  1. M.Sc. (Statistics), M.Sc. (Mathematics), M.Phil., Ph.D.

 Experience

No Experience Found....

 Expertise Information

Research Group
Statistics, Optimization and Discrete Mathematics
Areas of Interest
Number Theory, Nonlinear Optimization

 Projects

No Projects Found....

 Continuing Education

No Continuing Educations Found....

 Publications

Google Scholar h-index

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0

Scopus h-index

Total Publications: 44
P. K. Bhoi, S. S. Rout, and G. K. Panda, "On perfect powers that are sum of two balancing numbers", Periodica Mathematica Hungerica, Springer 2023, https://doi.org/10.1007/s10998-023-00540-7 Article
P. K. Bhoi, S. S. Rout, and G. K. Panda, "Sums of S-units in sum of terms of recurrence sequences", The Ramanujan Journal, Springer 2023, https://doi.org/10.1007/s11139-023-00756-8 Article
A. Patra, G. K. Panda, K. Onphaeng, P. Phunphayap, and T. Khemaratchatakumthorn, "Subsequences and Exact Divisibility by the Powers of the Balancing Numbers", International Journal of Mathematics and Computer Science, vol.17, no.2, pp.611-617, Lebanese University, Lebanon, February 2022 Article
Sai. G. Rayaguru and G. K. Panda, "Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers", The Journal of the Indian Mathematical Society, vol.89, no.1-2, pp.145-166, Indian Mathematical Society 2022, 10.18311/jims/2022/22177 Article
M. K. Sahukar, Z. Siar, R. Keskin, and G. K. Panda, "Perfect squares in the sum and difference of balancing-like numbers", Notes on Number Theory and Discrete Mathematics, vol.28, no.2, pp.286-301, Bulgarian Academy of Sciences 2022, 10.7546/nntdm.2022.28.2.286-301 Article

Show All Publications(+)

A. Patra and G. K. Panda, "Sums of finite products of Pell polynomials in terms of hypergeometric functions", Journal of the Egyptian Mathematical Society, vol.30, no.1, pp.1-20, Springer 2022, 10.1186/s42787-022-00137-y Article
Sai. G. Rayaguru, G. K. Panda, and Z. Siar, "Associated Pell numbers which are repdigits or concatenation of two repdigits", Boletín de la Sociedad Matemática Mexicana, vol.27, no.54, pp.article #7, Springer 2021, 10.1007/s40590-021-00360-0 Article
Sai. G. Rayaguru, G. K. Panda, and Z. Siar, "Associated Pell numbers which are repdigits or concatenation of two repdigits", Boletín de la Sociedad Matemática Mexicana, vol.27, no.2, pp.1-12, Springer 2021, 10.1007/s40590-021-00360-0 Article
Sai. G. Rayaguru and G. K. Panda, "Balancing and Lucas-balancing numbers expressible as sum of two repdigits", Integers, vol.21, no.a7, Colgate University 2021 Article
A. Patra, G. K. Panda, and T. Khemaratchatakumthorn, "Exact divisibility by powers of the balancing and lucas-balancing numbers", The Fibonacci Quarterly, vol.59, no.1, pp.57-64, The Fibonacci Association 2021 Article
A. Patra and G. K. Panda, "Exact divisibility by powers of the Pell and Associated Pell numbers", Proceedings - Mathematical Sciences, vol.131, pp.article #20, Springer 2021, 10.1007/s12044-021-00615-w Article
Sai. G. Rayaguru and G. K. Panda, "Repdigits as sums of two associated Pell numbers", Applied Mathematics E-notes, vol.21, pp.402-409, Tsing Hua University 2021 Article
G. K. Panda and M. K. Sahukar, "Repdigits in Euler functions of associated pell numbers", Proceeding--Mathematical Sciences, vol.130, no.25, Springer, March 2020, 10.1007/s12044-019-0551-3 Article
Sai. G. Rayaguru and G. K. Panda, "A generalization to almost balancing and cobalancing numbers using triangular numbers", Notes on Number Theory and Discrete Mathematics, vol.26, no.3, pp.135-148, Bulgarian Academy of Sciences 2020, 10.7546/nntdm.2020.26.3.135-148 Article
A. Patra and G. K. Panda, "Appearance of balancing and related number sequences in steady state probabilities of some Markov chains", Integers, vol.20a, no.a11, pp.1-13, Colgate University 2020 Article
G. K. Panda and S. S. Pradhan, "Associate sequences of a balancing-like sequence", Mathematical Reports, vol.22, no.3-4, pp.277-291, Romanian Academy 2020 Article
G. K. Panda and Sai. G. Rayaguru, "Balancing numbers which are concatenation of two repdigits", Boletín de la Sociedad Matemática Mexicana, vol.26, no.3, pp.911-919, Springer 2020, 10.1007/s40590-020-00293-0 Article
Sai. G. Rayaguru, R. K. Davala, and G. K. Panda, "Even-Odd balancing and cobalancing numbers", Proceedings of JANGJEON Mathematical Society, vol.23, no.3, pp.385-398, JANGJEON Mathematical Society 2020, 10.17777/pjms2020.23.3.385 Article
Sai. G. Rayaguru, J. Odjoumani, and G. K. Panda, "Factoriangular numbers in balancing and Lucas-balancing sequence", Boletín de la Sociedad Matemática Mexicana volume, vol.26, pp.865-878, Springer 2020, 10.1007/s40590-020-00303-1 Article
Sai. G. Rayaguru, M. K. Sahukar, and G. K. Panda, "Markov equation with components of some binary recurrent sequences", Notes on Number Theory and Discrete Mathematics, vol.26, no.3, pp.149-159, Academic Publishing House of the Bulgarian Academy of Sciences 2020, 10.7546/nntdm.2020.26.3.149-159 Article
A. Patra and G. K. Panda, "Positive integer solutions of some diophantine equations involving lucas-balancing numbers", The Fibonacci Quaterly, vol.58, no.1, pp.3-17, The Fibonacci Association 2020 Article
Sai. G. Rayaguru, G. K. Panda, and R., "Shift balancing numbers", Journal of the Indian Mathematical Society, vol.87, no.1-2, pp.131-136, Indian Mathematical Society 2020, 10.18311/jims/2020/24872 Article
S. S. Pradhan and G. K. Panda, "Sums of balancing-like sequences with binomial coefficients", Proceedings of JANGJEON Mathematical Society, vol.23, no.3, pp.421-432, JANGJEON Mathematical Society 2020 Article
A. Patra, T. Komatsu, and G. K. Panda, "The growth rate of random balancing sequence", Proceedings of the Jangjeon Mathematical Society, vol.23, no.3, pp.297-304, Jangjeon Mathematical Society 2020, 10.17777/pjms2020.23.3.297 Article
A. Patra and G. K. Panda, "Appearance of balancing and related number sequences in steady state probabilities of some Markov chains", Integers, vol.20a, no.a11, Colgate University, Charles University, and DIMATIA 2019 Article
M. K. Sahukar and G. K. Panda, "Balancing and balancing-like numbers which are one away from perfect powers", Bulletin of the Brazilian Mathematical Society, vol.51, pp.681-696, Springer 2019, 10.1007/s00574-019-00170-z Article
M. K. Sahukar and G. K. Panda, "Diophantine equations with balancing-like sequences associated to Brocard-Ramanujan-type problem.", Glasnik Matematicki, vol.54, no.2, pp.255-270., Croatian Mathematical Society 2019, https://doi.org/10.3336/gm.54.2.01 Article
Sai. G. Rayaguru, D. Savin, and G. K. Panda, "On some Horadam symbol elements", Notes on Number Theory and Discrete Mathematics, vol.25, no.2, pp.91-112, Bulgarian Academy of Sciences 2019, 10.7546/nntdm.2019.25.2.91-112 Article
R. K. Davala and G. K. Panda, "On sum and ratio formulas for Lucas-balancing numbers", Palestine Journal of Mathematics, vol.82, no.2, pp.200-206, Palestine Polytechnic University, Hebron 2019 Article
Sai. G. Rayaguru and G. K. Panda, "Repdigits as product of balancing and Lucas-balancing numbers with indices in arithmetic progressions", Fibonacci Quarterly, vol.57, no.3, pp.231--237, The Fibonacci Association 2019 Article
M. K. Sahukar and G. K. Panda, "Repdigits in Euler function of Pell numbers", Fibonacci Quarterly, vol.57, no.2, pp.134--138, The Fibonacci Association 2019 Article
Sai. G. Rayaguru and G. K. Panda, "Sum formulas involving powers of balancing and Lucas-balancing numbers", Journal of the Indian Mathematical Society, vol.86, no.1-2, pp.137-160, Informatics 2019, 10.18311/jims/2019/21623 Article
R. and G. K. Panda, "Sum formulas involving powers of balancing and Lucas-balancing numbers-II,", Notes on Number Theory and Discrete Mathematics, vol.25, no.3, pp.102-110, Bulgarian Academy of Sciences 2019, 10.7546/nntdm.2019.25.3.102-110 Article
G. K. Panda and S. S. Pradhan, "Triangular-like numbers that are triangular", The Fibonacci Quaterly, vol.57, no.4, pp.356-362, The Fibonacci Association 2019 Article
G. K. Panda and A. K. Panda, "Almost balancing numbers", Journal of the Indian Mathematical Society, vol.82, no.3-4, pp.147-156, Indian Mathematical Society 2015 Article
R. K. Davala and G. K. Panda, "On sum and ratio formulas for balancing numbers", Journal of the Indian Mathematical Society, vol.82, no.1-2, pp.23-32, Indian Mathematical Society 2015 Article
S. S. Rout and G. K. Panda, "Balancing Dirichlet series and related L-functions", Indian Journal of Pure and Applied Mathematics, vol.45, no.6, pp.943-952, Springer 2014, 10.1007/s13226-014-0097-0 Article
R. K. Davala and G. K. Panda, "On polygons with coordinates of vertices from Fibonacci and Lucas sequences", Journal for Geometry and Graphics, vol.18, no.2, pp.173-182, Heldermann Verlag 2014 Article
G. K. Panda and S. S. Rout, "Periodicity of balancing numbers", Acta Mathematica Hungarica, vol.143, no.2, pp.274-286, Springer 2014, 10.1007/s10474-014-0427-z Article
G. K. Panda and S. S. Rout, "Gap balancing numbers", Fibonacci Quarterly, vol.51, no.3, pp.239-248, The Fibonacci Association 2013 Article
G. K. Panda, "Sequence balancing and cobalancing numbers", Fibonacci Quarterly, vol.45, no.3, pp.265-271, The Fibonacci Association 2007 Article
B. Majhi, P. K. Sa, and G. K. Panda, "ANN based adaptive thresholding for impulse detection", in International Conference on Signal Processing, Pattern Recognition, and Applications, pp.294-297, ACTA, Innsbruck, Austria 2006 Inproceedings
G. K. Panda and P. K. Ray, "Cobalancing numbers and cobalancers", International Journal of Mathematics and Mathematical Sciences, vol.2005, no.8, pp.1189-1200, Hindawi Publishing Corporation 2005, 10.1155/IJMMS.2005.1189 Article
A. Behera and G. K. Panda, "On the square roots of triangular numbers", Fibonacci Quarterly, vol.37, no.2, pp.98-105, The Fibonacci Association 1999 Article

 Courses Taught

  • MA101 : Mathematics - I {Theory}
  • MA102 : Mathematics - II {Theory}
  • MA102 : Mathematics – II {Theory}
  • MA201 : Mathematics - III {Theory}
  • MA201 : Mathematics – III {Theory}
  • MA202 : Mathematics - IV {Theory}
  • MA202 : Mathematics – IV {Theory}
  • MA2203 : Introduction to Probability and Statistics {Theory}
  • MA2306 : Mathematical Methods {Theory}
  • MA3104 : Number Theory {Theory}
  • MA321 : Introduction to number Theory {Theory}
  • MA324 : Number Theory {Theory}
  • MA406 : Abstract Algebra {Theory}
  • MA427 : Elementary Number Theory {Theory}
  • MA524 : Statistical Methods {Theory}
  • MA555 : Stochastic Process {Theory}
  • MA556 : Number Theory {Theory}
  • MA558 : Sampling Techniques {Theory}
  • MA612 : Algebra {Theory}
  • MA623 : Advanced Number Theory {Theory}
  • MA625 : Stochastic Processes {Theory}
  • MA634 : Mathematical Methods {Theory}
  • MA655 : Mathematical Techniques for Data Analysis {Theory}
  • MA6623 : Advanced Number Theory {Theory}
  • MA270 : Numerical Methods Laboratory {Practical}
  • MA374 : Laboratory Work on Number Theory {Practical}
  • MA374 : Statistics Laboratory {Practical}
  • MA4272 : Statistics Laboratory {Practical}
  • MA471 : Object Oriented Programming Practice Laboratory {Practical}
  • MA481 : Departmental Seminar - I {Practical}
  • MA482 : Departmental Seminar - II {Practical}
  • MA571 : Statistics Laboratory {Practical}
  • MA572 : Laboratory Works on Sampling {Practical}

 Research Scholars

Ph.D. Students [14]
Generalized Variational Inequalities

 Niranjan Dash

Enrolled:

 Graduated : 

 Supervisor

Balancing and Cobalancing Numbers

 Prasanta Kumar Ray

Enrolled:

 Graduated : 

 Supervisor

Variational and Quasi-variational Inequalities

 Ganesh Kinkar Sahu

Enrolled:

 Graduated : 

 Supervisor

Number Theory

 Sudhansu Sekhar Rout

Enrolled: Jan 2011

 Graduated : Jul 2015

 Supervisor

A Study of Some Variational Inequalities

 Binaya Bhusan Sahoo

Enrolled:

 Graduated : 

 Supervisor

Some Variants of the Balancing Sequence

 Akshaya Kumar Panda

Enrolled: Jul 2012

 Graduated : Mar 2017

 Supervisor

Algebraic and Geometric Aspects of Some Binary Recurrence Sequences

 Ravi Kumar Davala

Enrolled: Jan 2013

 Graduated : Nov 2017

 Supervisor

A Study on Arithmetic Functions and Diophantine Equations Associated with Balancing and Related Sequences

 Manasi Kumari Sahukar

Enrolled: Jul 2015

 Graduated : Nov 2020

 Supervisor

Properties of Sequences and Sums associated with Balancing-like Sequences

 Sushree Sangeeta Pradhan

Enrolled: Jul 2015

 Graduated : Dec 2020

 Supervisor

Certain Sums, Products, Repdigits and Triples Associated with Balancing and Lucas-Balancing Numbers

 Sai Gopal Rayaguru

Enrolled: Jan 2016

 Graduated : Dec 2021

 Supervisor

Algebraic and Probabilistic Aspects of Some Binary Recurrence Sequences

 Asim Patra

Enrolled: Mar 2016

 Graduated : May 2023

 Supervisor

Number Theory

 Srikrishna Chandra Patel

Enrolled: Jul 2017

 Continuing

 Supervisor

NUMBER THEORY

 Pritam Kumar Bhoi

Enrolled: Jul 2019

 Continuing

 Supervisor

Number theory

 Monalisa Mohapatra

Enrolled: Jan 2023

 Continuing

 Supervisor

Executive Ph.D. Students [1]
Number Theory

 Gopal Sahu

 Continuing

 Supervisor

 Dissertations

PG Dissertation
  • Bibhudutta Dash (413MA2058), "A REVIEW OF FERMAT’S LAST THEOREM" - M.Sc.    Supervisor     2014-15 Spring
  • Juli Sahu (413MA2071), "k-BALANCING NUMBERS AND PELL’S EQUATION OF HIGHER ORDER" - M.Sc.    Supervisor     2014-15 Spring
  • Sephali Tanty (413MA2076), "Balancing And Lucas-balancing Numbers with Real Indices" - M.Sc.    Supervisor     2014-15 Spring
  • Debasis Sharma (415MA2087), "On new identities for the periodicity of balancing numbers." - M.Sc.    Supervisor     2016-17 Spring
  • Naseem (415MA2117), "On Split Balancing-like and Lucas Balancing-like Quaternions" - M.Sc.    Supervisor     2016-17 Spring
  • Prem Dagar (415MA2074), "Baire Category Theorem and its applications , Radon Nikodym Theorem and its applications" - M.Sc.    Co-supervisor     2016-17 Spring
  • Sharmila (415MA2072), "AGING PROPERTIES OF GENERALIZED-BETA AND GAMMA-GENERATED DISTRIBUTIONS" - M.Sc.    Co-supervisor     2016-17 Spring
  • Yogendra Sahu (415MA2085), "Gaussian Integer" - M.Sc.    Supervisor     2016-17 Spring
  • Jyotsna Ambast (419MA2081), "Bertrand Postulate and Goldbach Conjecture" - M.Sc.    Supervisor     2020-21 Spring
  • Tandrima Chowdhury (421MA2089), "Hurwitz Zeta Function Associated with Lucas Sequence and Multiple Hurwitz Zeta Function Associated with Lucas Sequence" - M.Sc.    Supervisor     2022-23 Spring
UG Dissertation
  • Kappagantu Prudhavi Nag (410MA5016), "SUM OF PRODUCT OF RECIPROCALS OF FIBONACCI NUMBERS" - Integrated M.Sc.    Supervisor     2014-15 Spring
  • Kadarla Manoj Kumar (411MA5108), "Balancing Numbers, Some Identities related to Balancing numbers." - Integrated M.Sc.    Supervisor     2015-16 Spring
  • Chowdary Umair Mukhtar (412MA5060), "NON-PARAMETRIC DENSITY ESTIMATION" - Integrated M.Sc.    Co-supervisor     2016-17 Spring
  • Nanda Khara (412MA5075), "Estimation of Unknown Parameters of Some Probability Models" - Integrated M.Sc.    Co-supervisor     2016-17 Spring
  • Bhaskar Behera (413MA5067), "Project Report on Properties of Periods of Balancing Sequence Modulo Primes" - Integrated M.Sc.    Supervisor     2017-18 Spring
  • Rahul Kumar (413MA5091), "Some Specifi cation on the Periodicity of Balancing Number Modulo Primes" - Integrated M.Sc.    Supervisor     2017-18 Spring
  • Pritam Kumar Sahu (414MA5056), "Statistical Aspect of Some Number Sequences" - Integrated M.Sc.    Supervisor     2018-19 Spring
  • Satyabrat Rath (414MA5073), "Number of Classes and Classifi cation of Circular Balancing Numbers" - Integrated M.Sc.    Supervisor     2018-19 Spring
  • Shubham Sourav Meher (414MA5070), "A study of some Pell's equation associated with almost balancing-like sequence." - Integrated M.Sc.    Supervisor     2018-19 Spring
  • Ashutosh Kumar Gupta (415MA5085), "Some Generalizations of Balancing Numbers and Perfect Balancing Numbers." - Integrated M.Sc.    Supervisor     2019-20 Spring
  • Lalatendu Bidyadhar Sahoo (415MA5029), "APPROXIMATION AND ALGEBRAIC ASPECTS OF NUMBER THEORY" - Integrated M.Sc.    Supervisor     2019-20 Spring
  • Nookala Ravali (415MA5027), "APPLICATIONS OF CRYPTOGRAPHY AND DIOPHANTINE EQUATIONS" - Integrated M.Sc.    Supervisor     2019-20 Spring
  • Prithviraj Das Mohapatra (416MA5033), "Elliptic Curve Diffie-Hellman Algorithm" - Integrated M.Sc.    Supervisor     2020-21 Spring
  • Arijit Singh (417MA5019), "Cryptography using Fibonacci and Pell sequences with Affine Hill cipher" - Integrated M.Sc.    Supervisor     2021-22 Spring
  • Suman Kumar (417MA5066), "Some properties of balancing number and related sequences" - Integrated M.Sc.    Supervisor     2021-22 Spring
  • Jerin James (418MA5017), "Comparison of Cryptographic Algorithms in Image Encryption using DNA Encoding." - Integrated M.Sc.    Supervisor     2022-23 Spring
  • Yamir Ahsan (418MA5016), "A Study on Properties and Application of Jacobsthal Sequence." - Integrated M.Sc.    Supervisor     2022-23 Spring

 Awards and Honours

Awards and Honours
  • 1. University gold medal for securing first position in first class in M.A./M.Sc.(Statistics) from Sambalpur University in the year 1985. 2. Gangadhar Meher Silver Jubilee gold medal for securing highest percent of marks in total aggregate at B.A./B.Sc./B.Com./M.A./M.Sc./M.Com. examinations of Sambalpur University in the year 1985. 3. Merit certificate for securing first position in first class in B.Sc. Statistics Honours from Sambalpur University in the year 1983.,   
Memberships / Fellowships
  • Life Member of Computer Society of India and Odisha Mathematical Society,