Bijan Kumar Patel

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All published works

Action	Title	Year	Authors
+	ON PERFECT POWERS AS SUMS OR DIFFERENCES OF TWO <i>k</i>-GENERALISED PELL NUMBERS	2025	Bijan Kumar Patel Bibhu Prasad Tripathy
+ PDF Chat	Sums of Three Fibonacci Numbers Close to a Power of 2	2023	Bibhu Prasad Tripathy Bijan Kumar Patel
+	$k$-Pell-Lucas numbers which are concatenations of two repdigits	2023	Bibhu Prasad Tripathy Bijan Kumar Patel
+	Common terms of generalized Pell and Narayana's cows sequences	2023	Bibhu Prasad Tripathy Bijan Kumar Patel
+ PDF Chat	Narayana numbers as sums of two base b repdigits	2022	Prasanta Kumar Ray Kisan Bhoi Bijan Kumar Patel
+	Nonlinear identities and Diophantine equations involving balancing-like and Lucas-balancing-like numbers	2022	Asim Patra Claudio Pita-Ruiz Bijan Kumar Patel
+	On the Exponential Diophantine Equation $(F_{m+1}^{(k)})^x-(F_{m-1}^{(k)})^x = F_n^{(k)}$	2022	Hayat Bensella Bijan Kumar Patel Djilali Behloul
+	Sums of three Fibonacci numbers close to a power of 2	2022	Bibhu Prasad Tripathy Bijan Kumar Patel
+	$k$-Pell-Lucas numbers as Product of Two Repdigits	2022	Bibhu Prasad Tripathy Bijan Kumar Patel
+	On the Exponential Diophantine Equation $$F_{n+1}^{x} - F_{n-1}^{x} = F_{m}$$	2021	Bijan Kumar Patel Ana Paula Chaves
+	On a Generalization of Incomplete Fibonacci Quaternions	2021	Bijan Kumar Patel N. Behera
+ PDF Chat	Several formulas for Bernoulli numbers and polynomials	2021	Takao Komatsu Bijan Kumar Patel Claudio Pita-Ruiz
+	Diophantine Equation with Balancing-like Sequences Associated to the Pillai-Tijdeman-type Problem	2021	Bijan Kumar Patel Prashant Kumar Tiwari
+	An Exponential Diophantine Equation Related to Powers of Three Consecutive Fibonacci Numbers	2020	Bijan Kumar Patel Wen Chean Teh
+	Pell and Pell-Lucas numbers as sums of three repdigits	2020	Kisan Bhoi Bijan Kumar Patel Prasanta Kumar Ray
+	Balancing non-Wieferich primes in arithmetic progressions	2019	Utkal Keshari Dutta Bijan Kumar Patel Prasanta Kumar Ray
+ PDF Chat	On the convergence of second-order recurrence series	2018	Bijan Kumar Patel Prasanta Kumar Ray
+	Period of balancing numbers modulo product of consecutive Lucas-balancing numbers	2018	Bijan Kumar Patel Shanta Kumari Sunanda Prasanta Kumar Ray
+	The rank of apparition of powers of Lucas sequence	2018	Prasanta Kumar Ray Nurettin Irmak Bijan Kumar Patel
+	A brief remark on balancing-Wieferich primes	2018	Utkal Keshari Dutta Bijan Kumar Patel Prasanta Kumar Ray
+	Incomplete balancing and lucas-balancing numbers	2018	Bijan Kumar Patel Nurettin Irmak Prasanta Kumar Ray Alexandru Zaharescu
+ PDF Chat	Uniform Distribution of the Sequence of Balancing Numbers Modulo <i>m</i>	2016	Prasanta Kumar Ray Bijan Kumar Patel
+	Solutions Of Some Non-Linear Programming Problems	2014	Bijan Kumar Patel

Common Coauthors

Coauthor	Papers Together
Prasanta Kumar Ray	9
Bibhu Prasad Tripathy	6
Nurettin Irmak	2
Utkal Keshari Dutta	2
Kisan Bhoi	2
Hayat Bensella	1
Djilali Behloul	1
Prashant Kumar Tiwari	1
N. Behera	1
Claudio Pita-Ruiz	1
Takao Komatsu	1
Asim Patra	1
Shanta Kumari Sunanda	1
Claudio Pita-Ruiz	1
Wen Chean Teh	1
Alexandru Zaharescu	1
Ana Paula Chaves	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On the Square Roots of Triangular Numbers	1999	Ajay Kumar Behera G. K. Panda	6
+ PDF Chat	Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers	2006	Yann Bugeaud Maurice Mignotte Samir Siksek	5
+	Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications.	2014	Prasanta Kumar Ray	4
+	A Generalization of a Theorem of Baker and Davenport	1998	Andrej Dujella A. Petho	4
+	Periodicity of Balancing Numbers	2014	G. K. Panda Sudhansu Sekhar Rout	4
+	An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II	2000	E M Matveev	4
+	An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers	1998	E M Matveev	3
+	A Diophantine equation related to the sum of powers of two consecutive generalized Fibonacci numbers	2015	Ana Paula Chaves Diego Marques	2
+ PDF Chat	On the Diophantine Equation <i>n</i>(<i>n</i> + <i>d</i>) · · · (<i>n</i> + (<i>k</i> − 1)<i>d</i>) = <i>by</i><sup><i>l</i></sup>	2004	Kálmán Győry Lajos Hajdu N. Saradha	2
+ PDF Chat	On the sum of powers of two consecutive Fibonacci numbers	2010	Diego Marques Alain Togbé	2
+ PDF Chat	An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers	2014	Carlos A. Gómez Florian Luca	2
+	Fibonacci and Lucas numbers with only one distinct digit.	2000	Florian Luca	2
+	Formes linéaires en deux logarithmes et déterminants d′interpolation	1995	Laurent Michel Maurice Mignotte Yuri Valentinovich Nesterenko	2
+	A generalization of a theorem of Baker and Davenport	1998	Andrej Dujella Attila Pethö	2
+	Fibonacci and Lucas Numbers with Applications	2017	Thomas Koshy	2
+	Balancing and Cobalancing Numbers	2009	Prasanta Kumar Ray	2
+	The Diophantine equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mi>a</mml:mi><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>b</mml:mi><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo…	2013	Zhongfeng Zhang	2
+	On the Diophantine equation $F_n^x+F_{n+1}^x=F_m^y$	2015	Noriko Hirata-Kohno Florian Luca	2
+	Some Facinating Properties of Balancing Numbers	2006	G. K. Panda	2
+	Pell and Pell–Lucas Numbers with Applications	2014	Thomas Koshy	2
+	On the properties of k-balancing numbers	2016	Prasanta Kumar Ray	2
+	Upper bounds for solutions of an exponential Diophantine equation	2015	Takafumi Miyazaki	2
+	On the sum of squares of consecutive $k$-bonacci numbers which are $l$-bonacci numbers	2019	Dušan Bednařı́k Gérsica Freitas Diego Marques Pavel Trojovský	2
+	Balancing non-Wieferich primes in arithmetic progression and $abc$ conjecture	2016	Sudhansu Sekhar Rout	2
+	Fibonacci and Lucas Numbers With Applications	2018	Thomas Koshy	2
+	Lucas numbers as sums of two repdigits	2019	Chèfiath Adegbindin Florian Luca Alain Togbé	2
+ PDF Chat	An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers	2011	Florian Luca Roger Oyono	2
+	Pell and Pell-Lucas numbers with only one distinct digit	2015	Bernadette Faye Florian Luca	2
+	The Order of Appearance of the Product of Consecutive Lucas Numbers	2013	Diego Marques	2
+	On integers with identical digits	1999	Yann Bugeaud Maurice Mignotte	1
+	Incomplete Fibonacci and Lucas numbers	1996	Piero Filipponi	1
+ PDF Chat	On a Conjecture Regarding Balancing with Powers of Fibonacci Numbers	2012	Saúl Díaz Alvarado Andrej Dujella Florian Luca	1
+	Explicit Formulas for Bernoulli Numbers	1972	H. W. Gould	1
+ PDF Chat	The Order of Appearance of the Product of Five Consecutive Lucas Numbers	2014	Diego Marques Pavel Trojovský	1
+	Generating functions of the incomplete Fibonacci and Lucas numbers	1999	Ákos Pintér H. M. Srivastava	1
+ PDF Chat	Fibonacci numbers at most one away from a perfect power	2008	Yann Bugeaud Florian Luca Maurice Mignotte Samir Siksek	1
+ PDF Chat	Powers in products of terms of Pell's and Pell–Lucas Sequences	2014	Jhon J. Bravo Pranabesh Das Sergio Guzmán Shanta Laishram	1
+	On a conjecture about repdigits in k-generalized Fibonacci sequences	2013	Jhon J. Bravo Florian Luca	1
+ PDF Chat	Uniform distribution of sequences of integers	1961	Ivan Niven	1
+	A connection between Jacobi–Stirling numbers and Bernoulli polynomials	2015	Mircea Merca	1
+	The Fibonacci sequence modulo $p^2$ -- An investigation by computer for $p < 10^{14}$	2010	Andreas-Stephan Elsenhans Jörg Jahnel	1
+	On the Numerical Factors of the Arithmetic Forms α n ± β n	1913	R. D. Carmichael	1
+ PDF Chat	A search for Fibonacci-Wieferich and Wolstenholme primes	2007	Richard J. McIntosh E. L. Roettger	1
+ PDF Chat	On terms of linear recurrence sequences with only one distinct block of digits	2011	Diego Marques Alain Togbé	1
+	Incomplete Generalized Fibonacci and Lucas Polynomials	2013	Jósé L. Ramírez	1
+	Non-Wieferich primes in arithmetic progressions	2016	Yong-Gao Chen Yuchen Ding	1
+	Fibonacci Series Modulo <i>m</i>	1960	D. D. Wall	1
+	Connections between central factorial numbers and Bernoulli polynomials	2016	Mircea Merca	1
+ PDF Chat	THE EQUATIONS 3<i>x</i><sup>2</sup>−2 = <i>y</i><sup>2</sup> AND 8<i>x</i><sup>2</sup>−7 = <i>z</i><sup>2</sup>	1969	A. Baker H. Davenport	1
+	A new connection between<i>r</i>-Whitney numbers and Bernoulli polynomials	2014	Mircea Merca	1