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11B39 Fibonacci and Lucas numbers and polynomials and generalizations (57 articles)

• Schwab, Emil Daniel; Schwab, Gabriela: A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions. (English). Mathematica Bohemica, vol. 149 (2024), issue 2, pp. 237-246
• Bród, Dorota; Szynal-Liana, Anetta: On generalized bihyperbolic Mersenne numbers. (English). Mathematica Bohemica, vol. 149 (2024), issue 1, pp. 75-85
• Şiar, Zafer; Keskin, Refik; Öztaş, Elif Segah: On perfect powers in $k$-generalized Pell sequence. (English). Mathematica Bohemica, vol. 148 (2023), issue 4, pp. 507-518
• Adédji, Kouèssi Norbert; Odjoumani, Japhet; Togbé, Alain: Padovan and Perrin numbers as products of two generalized Lucas numbers. (English). Archivum Mathematicum, vol. 59 (2023), issue 4, pp. 315-337
• Du, Zhibin; da Fonseca, Carlos M.: Root location for the characteristic polynomial of a Fibonacci type sequence. (English). Czechoslovak Mathematical Journal, vol. 73 (2023), issue 1, pp. 189-195
• Hashim, Hayder R.: Bartz-Marlewski equation with generalized Lucas components. (English). Archivum Mathematicum, vol. 58 (2022), issue 3, pp. 189-197
• Alzer, Horst; Luca, Florian: An inequality for Fibonacci numbers. (English). Mathematica Bohemica, vol. 147 (2022), issue 4, pp. 587-590
• Hashim, Hayder Raheem; Tengely, Szabolcs: Lucas sequences and repdigits. (English). Mathematica Bohemica, vol. 147 (2022), issue 3, pp. 301-318
• Alan, Murat: Mersenne numbers as a difference of two Lucas numbers. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 63 (2022), issue 3, pp. 269-276
• Bród, Dorota; Szynal-Liana, Anetta; Włoch, Iwona: On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. (English). Czechoslovak Mathematical Journal, vol. 72 (2022), issue 4, pp. 1239-1248
• Bród, Dorota; Szynal-Liana, Anetta; Włoch, Iwona: Bihyperbolic numbers of the Fibonacci type and their idempotent representation. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 62 (2021), issue 4, pp. 409-416
• Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian: On a generalization of the Pell sequence. (English). Mathematica Bohemica, vol. 146 (2021), issue 2, pp. 199-213
• Patel, Bijan Kumar; Ray, Prasanta Kumar: On Balancing and Lucas-balancing Quaternions. (English). Communications in Mathematics, vol. 29 (2021), issue 3, pp. 325-341
• Tchammou, Euloge; Togbé, Alain: On some Diophantine equations involving balancing numbers. (English). Archivum Mathematicum, vol. 57 (2021), issue 2, pp. 113-130
• Tong, Ruizhou: On the Diophantine equation $(2^x-1)(p^y-1)=2z^2$. (English). Czechoslovak Mathematical Journal, vol. 71 (2021), issue 3, pp. 689-696
• Gómez, Carlos A.; Luca, Florian: On the distribution of the roots of polynomial $z^k-z^{k-1}-\dots - z-1$. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 62 (2021), issue 3, pp. 291-296
• Luca, Florian; Manganye, Sylvester: On the gaps between $q$-binomial coefficients. (English). Communications in Mathematics, vol. 29 (2021), issue 3, pp. 431-442
• Keskin, Refik; Erduvan, Fatih: Repdigits in the base $b$ as sums of four balancing numbers. (English). Mathematica Bohemica, vol. 146 (2021), issue 1, pp. 55-68
• Agnihotri, Rishabh; Chakraborty, Kalyan: Sign changes of certain arithmetical function at prime powers. (English). Czechoslovak Mathematical Journal, vol. 71 (2021), issue 4, pp. 1221-1228
• Paja, Natalia; Włoch, Iwona: Some interpretations of the $(k,p)$-Fibonacci numbers. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 62 (2021), issue 3, pp. 297-307
• Adegbindin, Chèfiath A.; Togbé, Alain: Can a Lucas number be a sum of three repdigits?. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 61 (2020), issue 3, pp. 383-396
• Bravo, Jhon J.; Herrera, Jose L.: Fermat $k$-Fibonacci and $k$-Lucas numbers. (English). Mathematica Bohemica, vol. 145 (2020), issue 1, pp. 19-32
• Kafle, Bir; Luca, Florian; Togbé, Alain: Lucas factoriangular numbers. (English). Mathematica Bohemica, vol. 145 (2020), issue 1, pp. 33-43
• Qu, Yunyun; Zeng, Jiwen: Pell and Pell-Lucas numbers of the form $-2^a-3^b+5^c$. (English). Czechoslovak Mathematical Journal, vol. 70 (2020), issue 1, pp. 281-289
• Bravo, Jhon J.; Herrera, Jose L.: Repdigits in generalized Pell sequences. (English). Archivum Mathematicum, vol. 56 (2020), issue 4, pp. 249-262
• Hashim, Hayder R.: Solutions of the Diophantine Equation $7X^2+Y^7=Z^2$ from Recurrence Sequences. (English). Communications in Mathematics, vol. 28 (2020), issue 1, pp. 55-66
• Öcalan, Özkan; Duman, Oktay: Solutions to conjectures on a nonlinear recursive equation. (English). Czechoslovak Mathematical Journal, vol. 70 (2020), issue 3, pp. 867-880
• Soydan, Gökhan; Németh, László; Szalay, László: On the Diophantine equation $\sum _{j=1}^kjF_j^p=F_n^q$. (English). Archivum Mathematicum, vol. 54 (2018), issue 3, pp. 177-188
• Szakács, Tamás: Convolution of second order linear recursive sequences II. (English). Communications in Mathematics, vol. 25 (2017), issue 2, pp. 137-148
• Snášel, Václav; Bouchala, Jiří; Vodstrčil, Petr: Kouzlo Fibonacciho kódování. (Czech) [The magic of Fibonacci codes]. Pokroky matematiky, fyziky a astronomie, vol. 61 (2016), issue 3, pp. 234-242
• Euler, Reinhardt; Gallardo, Luis H.; Luca, Florian: On a binary recurrent sequence of polynomials. (English). Communications in Mathematics, vol. 22 (2014), issue 2, pp. 151-157
• Keskin, Refik; Şiar, Zafer; Karaatlı, Olcay: On the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$. (English). Czechoslovak Mathematical Journal, vol. 63 (2013), issue 3, pp. 783-797
• Marques, Diego: On the intersection of two distinct $k$-generalized Fibonacci sequences. (English). Mathematica Bohemica, vol. 137 (2012), issue 4, pp. 403-413
• Klaška, Jiří: Criteria for testing Wall's question. (English). Czechoslovak Mathematical Journal, vol. 58 (2008), issue 4, pp. 1241-1246
• Griffin, Kent; Stuart, Jeffrey L.; Tsatsomeros, Michael J.: Noncirculant Toeplitz matrices all of whose powers are Toeplitz. (English). Czechoslovak Mathematical Journal, vol. 58 (2008), issue 4, pp. 1185-1193
• Klaška, Jiří: A search for Tribonacci-Wieferich primes. (English). Acta Mathematica Universitatis Ostraviensis, vol. 16 (2008), issue 1, pp. 15-20
• Klaška, Jiří: Tribonacci modulo $2^t$ and $11^t$. (English). Mathematica Bohemica, vol. 133 (2008), issue 4, pp. 377-387
• Klaška, Jiří: Tribonacci modulo $p^t$. (English). Mathematica Bohemica, vol. 133 (2008), issue 3, pp. 267-288
• Carlip, Walter; Somer, Lawrence: Bounds for frequencies of residues of second-order recurrences modulo $p^r$. (English). Mathematica Bohemica, vol. 132 (2007), issue 2, pp. 137-175
• Klaška, Jiří: Short remark on Fibonacci-Wieferich primes. (English). Acta Mathematica Universitatis Ostraviensis, vol. 15 (2007), issue 1, pp. 21-25
• Carlip, W.; Somer, L.: Square-free Lucas $d$-pseudoprimes and Carmichael-Lucas numbers. (English). Czechoslovak Mathematical Journal, vol. 57 (2007), issue 1, pp. 447-463
• Seibert, Jaroslav; Trojovský, Pavel: Circulants and the factorization of the Fibonacci–like numbers. (English). Acta Mathematica Universitatis Ostraviensis, vol. 14 (2006), issue 1, pp. 63-70
• Orosz, Erzsébet: Common terms in binary recurrences. (English). Acta Mathematica Universitatis Ostraviensis, vol. 14 (2006), issue 1, pp. 57-61
• Ericksen, Larry: Iterated digit sums, recursions and primality. (English). Acta Mathematica Universitatis Ostraviensis, vol. 14 (2006), issue 1, pp. 27-35
• Liptai, Kálmán: Lucas balancing numbers. (English). Acta Mathematica Universitatis Ostraviensis, vol. 14 (2006), issue 1, pp. 43-47
• Křížek, Michal; Luca, Florian; Somer, Lawrence: Aritmetické vlastnosti Fibonacciových čísel. (Czech) [Arithmetic properties of Fibonacci numbers]. Pokroky matematiky, fyziky a astronomie, vol. 50 (2005), issue 2, pp. 127-140
• Seibert, Jaroslav; Trojovský, Pavel: On some identities for the Fibonomial coefficients. (English). Mathematica Slovaca, vol. 55 (2005), issue 1, pp. 9-19
• Rotkiewicz, A.: On Lucas pseudoprimes of the form $ax^2+bxy+cy^2$ in arithmetic progression $AX+B$ with a prescribed value of the Jacobi symbol. (English). Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 10 (2002), issue 1, pp. 103-109
• Mátyás, Ferenc: Sequence transformations and linear recurrences of higher order. (English). Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 9 (2001), issue 1, pp. 45-51
• Messaoudi, Ali: Généralisation de la multiplication de Fibonacci. (French) [Generalization of the Fibonacci multiplication]. Mathematica Slovaca, vol. 50 (2000), issue 2, pp. 135-148
• Rotkiewicz, Andrzej: Arithmetic progressions formed by pseudoprimes. (English). Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 8 (2000), issue 1, pp. 61-74
• Jones, James P.; Kiss, Péter: Some Diophantine approximation results concerning linear recurrences. (English). Mathematica Slovaca, vol. 42 (1992), issue 5, pp. 583-591
• Mikhailov, I. I.: Об одном свойстве фигурных чисел. (Russian) [A property of figurate numbers]. Mathematica Slovaca, vol. 33 (1983), issue 3, pp. 303-306
• Selucký, Konstantin; Skula, Ladislav: Irregular imaginary fields. (English). Archivum Mathematicum, vol. 17 (1981), issue 2, pp. 95-112
• Skula, Ladislav: On certain ideals of the group ring $\bold Z [G]$. (English). Archivum Mathematicum, vol. 15 (1979), issue 1, pp. 53-66
• Karpe, Robert: Die Kombinationen gegebenen Profils. III. (German) [The combinations of given profiles. III]. Archivum Mathematicum, vol. 10 (1974), issue 4, pp. 199-220
• Karpe, Robert: Algorithmus für Bell'sche Polynome. (German) [An algorithm for Bell's plynomials]. Archivum Mathematicum, vol. 8 (1972), issue 1, pp. 45-50