Found 166 Documents (Results 1–100)
Transcendental simplicial volumes. (Volumes Simpliciaux Transcendantaux.) (English. French summary) Zbl 07852669
A Diophantine equation with powers of three consecutive \(k\)-Fibonacci numbers. (English) Zbl 1539.11033
Reviewer: Mahadi Ddamulira (Kampala)
The complete solution of the Diophantine equation \(\left(F_{n+1}^{(k)}\right)^x - \left(F_{n-1}^{(k)}\right)^x = F_m^{(k)}\). (English) Zbl 1534.11022
Reviewer: Mahadi Ddamulira (Kampala)
On the representation of an integer in Ostrowski and recurrence numeration systems. arXiv:2409.06232
Preprint, arXiv:2409.06232 [math.NT] (2024).
On the solutions of the Diophantine equation \(P_n \pm \frac{a(10^m -1)}{9}=k!\). (English) Zbl 1530.11020
Reviewer: Mahadi Ddamulira (Kampala)
On the representation of an imaginary quadratic integer in two different bases. arXiv:2311.17348
Preprint, arXiv:2311.17348 [math.NT] (2023).
The problem of the extension of \(D(4)\)-triple \(\{1, b, c\}\). (English) Zbl 1523.11056
Reviewer: Mahadi Ddamulira (Kampala)
On the solutions of the Diophantine equation \(F_n \pm \frac{a (10^m - 1)}{9} = k!\). (English) Zbl 1498.11106
Reviewer: Mahadi Ddamulira (Kampala)
The extension of the \(D(-k)\)-triple \(\{1,k,k+1\}\) to a quadruple. (English) Zbl 1513.11104
Reviewer: Nikos Tzanakis (Iraklion)
Transcendental number theory. With a new foreword by David Masser. Reprint of the 1990 paperback edition. (English) Zbl 1496.11001
Cambridge Mathematical Library. Cambridge: Cambridge University Press (ISBN 978-1-00-922994-4/pbk; 978-1-00-922993-7/ebook). xiv, 169 p. (2022).
Diophantine approximation. (English. Japanese original) Zbl 1489.11102
Sugaku Expo. 34, No. 2, 205-229 (2021); translation from Sūgaku 64, No. 3, 254-277 (2012).
Reviewer: Clemens Fuchs (Salzburg)
Irrationality measures for cubic irrationals whose conjugates Lie on a curve. (English) Zbl 1480.11092
Reviewer: Jaroslav Hančl (Ostrava)
On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. II. (English) Zbl 1493.11074
Reviewer: Ilker Inam (Bilecik)
On the zero-multiplicity of the \(k\)-generalized Fibonacci sequence. (English) Zbl 1464.11024
Reviewer: Mahadi Ddamulira (Kampala)
Multiplicative dependence between \(k\)-Fibonacci and \(k\)-Lucas numbers. (English) Zbl 1474.11047
Reviewer: Štefan Porubský (Praha)
On the discriminants of the powers of an algebraic integer. (English) Zbl 1441.11270
Reviewer: István Gaál (Debrecen)
Thue Diophantine equations. (English) Zbl 1456.11034
Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer. 25-41 (2020).
Reviewer: Nikos Tzanakis (Iraklion)
The zero-multiplicity of Berstel type sequences. (English) Zbl 1463.11036
Reviewer: Michel Waldschmidt (Paris)
Product of consecutive tribonacci numbers with only one distinct digit. (English) Zbl 1455.11027
Reviewer: István Gaál (Debrecen)
On the zero-multiplicity of a fifth-order linear recurrence. (English) Zbl 1450.11009
Reviewer: Artūras Dubickas (Vilnius)
Contributions to some conjectures on a ternary exponential Diophantine equation. (English) Zbl 1428.11062
Reviewer: Florian Luca (Johannesburg)
Computing relative power integral bases in a family of quartic extensions of imaginary quadratic fields. (English) Zbl 1399.11097
Reviewer: István Gaál (Debrecen)
Linear forms in logarithms and applications. (English) Zbl 1394.11001
IRMA Lectures in Mathematics and Theoretical Physics 28. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-183-5/pbk; 978-3-03719-683-0/ebook). xvi, 224 p. (2018).
Reviewer: István Gaál (Debrecen)
Effective irrationality measures for real and \(p\)-adic roots of rational numbers close to \(1\), with an application to parametric families of Thue-Mahler equations. (English) Zbl 1439.11172
Reviewer: Michel Waldschmidt (Paris)
Fibonacci factoriangular numbers. (English) Zbl 1373.11011
Reviewer: Sandi Klavžar (Ljubljana)
MSC:
11B39
On a conjecture of Livingston. (English) Zbl 1422.11161
Multiplicative Diophantine equations with factors from different Lucas sequences. (English) Zbl 1402.11025
Proof of Serge Lang’s Heights Conjecture and an almost optimal Bound for the Torsion of Elliptic Curves. arXiv:1701.07433
Preprint, arXiv:1701.07433 [math.NT] (2017).
MSC:
11G50
11D75
11D99
11G05
11G07
11G99
11H99
11J25
11J68
11J81
11J82
11J86
11J99
14G05
14G22
14G25
14G40
14G99
14H52
14H99
14J20
14K15
On the largest prime factor of the ratio of two generalized Fibonacci numbers. (English) Zbl 1393.11012
Diophantine quadruples in the sequence of shifted Tribonacci numbers. (English) Zbl 1349.11024
Reviewer: Lajos Hajdu (Debrecen)
Tribonacci numbers, \(S\)-units and Diophantine triples. (Spanish. English summary) Zbl 1393.11011
Multiplicatively dependent triples of Tribonacci numbers. (English) Zbl 1350.11020
Reviewer: Lajos Hajdu (Debrecen)
On elements with index of the form \(2^a3^b\) in a parametric family of biquadratic fields. (English) Zbl 1387.11026
On the system of Diophantine equations \((m^2 - 1)^r + b^2 = c^2\) and \((m^2 - 1)^x + b^y = c^z\). (English) Zbl 1365.11033
\(k\)-generalized Fibonacci numbers of the form \(1+2^{n_1}+4^{n_2}+\cdots +(2^{k})^{n_k}\). (English) Zbl 1323.11012
Reviewer: Olaf Ninnemann (Berlin)
An exponential Diophantine equation related to the sum of powers of two consecutive \(k\)-generalized Fibonacci numbers. (English) Zbl 1338.11016
A note on the article by F. Luca “On the system of Diophantine equations \(a^2+b^2=(m^2+1)^r\) and \(a^x+b^y=(m^2+1)^z\)”. (English) Zbl 1300.11027
The zero-multiplicity of third-order linear recurrences associated to the Tribonacci sequence. (English) Zbl 1297.39002
Transcendental numbers. (English) Zbl 1297.11001
New York, NY: Springer (ISBN 978-1-4939-0831-8/pbk; 978-1-4939-0832-5/ebook). xiv, 217 p. (2014).
Reviewer: Werner Kleinert (Berlin)
Coincidences in generalized Fibonacci sequences. (English) Zbl 1272.11028
J. Number Theory 133, No. 6, 2121-2137 (2013); corrigendum ibid. 133, No. 9, 3205 (2013).
Reviewer: Thomas Stoll (Vandœuvre-lés Nancy)
On the distance between products of consecutive Fibonacci numbers and powers of Fibonacci numbers. (English) Zbl 1282.11010
Reviewer: István Pink (Debrecen)
On \(D(-1)\)-quadruples. (English) Zbl 1354.11024
Approximation of an algebraic number by products of rational numbers and units. (English) Zbl 1300.11026
Reviewer: Maurice Mignotte (Strasbourg)
The non-extendibility of some parametric families of \(D(-1)\)-triples. (English) Zbl 1255.11015
Reviewer: Mihai Cipu (Bucureşti)
Some remarks concerning the rank of mapping tori and ascending HNN-extensions of Abelian groups. (English. Italian summary) Zbl 1286.20032
Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 23, No. 2, 197-211 (2012).
Reviewer: Thomas Koberda (New Haven)
The number of Diophantine quintuples. (English) Zbl 1211.11040
Reviewer: Andrej Dujella (Zagreb)
Corrigendum to “Transcendence of the log gamma function and some discrete periods”. (English) Zbl 1216.11070
Computing partial information out of intractable: powers of algebraic numbers as an example. (English) Zbl 1251.11052
Reviewer: Maurice Mignotte (Strasbourg)
Arithmetic properties of the integer part of the powers of an algebraic number. (English) Zbl 1234.11098
Reviewer: Artūras Dubickas (Vilnius)
Establishing the minimal index in a parametric family of bicyclic biquadratic fields. (English) Zbl 1265.11061
On the family of Diophantine triples \(\{k+1,4k,9k+3\}\). (English) Zbl 1199.11075
Reviewer: Lajos Hajdu (Debrecen)
Transcendence of the log gamma function and some discrete periods. (English) Zbl 1175.11039
J. Number Theory 129, No. 9, 2154-2165 (2009); corrigendum ibid. 130, No. 5, 1251 (2010).
Reviewer: Michel Waldschmidt (Paris)
Linear forms in the logarithms of algebraic numbers close to 1 and applications to Diophantine equations. (English) Zbl 1194.11079
Saradha, N. (ed.), Diophantine equations. Papers from the international conference held in honor of T. N. Shorey’s 60th birthday, Mumbai, India, December 16–20, 2005. New Delhi: Narosa Publishing House/Published for the Tata Institute of Fundamental Research (ISBN 978-81-7319-898-4/hbk). Studies in Mathematics. Tata Institute of Fundamental Research 20, 59-76 (2008).
Reviewer: Michel Waldschmidt (Paris)
Fibonacci numbers at most one away from a perfect power. (English) Zbl 1156.11008
Reviewer: Nikos Tzanakis (Iraklion)
\(p\)-adic logarithmic forms and group varieties. III. (English) Zbl 1132.11038
Reviewer: Michel Waldschmidt (Paris)
The \(D(1)\)-extensions of \(D(-1)\)-triples \(\{ 1,2,c \}\) and integer points on the attached elliptic curves. (English) Zbl 1152.11013
Reviewer: Liang-Chung Hsia (Taiwan)
Index of lattices and Hilbert polynomials. (English. Russian original) Zbl 1116.11047
Math. Notes 80, No. 3, 313-317 (2006); translation from Mat. Zametki 80, No. 3, 323-327 (2006).
Reviewer: Michel Waldschmidt (Paris)
Explicit lower bounds for liner forms in two logarithms. (English) Zbl 1119.11040
Reviewer: Maurice Mignotte (Strasbourg)
MSC:
11J86
Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers. (English) Zbl 1113.11021
Reviewer: Wolfgang Schwarz (Frankfurt / Main)
Hilbert’s seventh problem. (English) Zbl 1152.11035
Bolibruch, A.A. (ed.) et al., Mathematical events of the twentieth century. Transl. from the Russian. Berlin: Springer; Moscow: PHASIS (ISBN 3-540-23235-4/hbk). 269-282 (2006).
Reviewer: Leon Harkleroad (Wilton)
The index of multiplicative groups of algebraic numbers. (English) Zbl 1141.11049
Sb. Math. 196, No. 9, 1307-1318 (2005); translation from Mat. Sb. 196, No. 9, 59-70 (2005).
Reviewer: Artūras Dubickas (Vilnius)
Some ideas on computational Diophantine equations. (Quelques idées sur l’algorithmique des équations diophantiennes.) (French) Zbl 1119.11025
Berline, Nicole (ed.) et al., Computational number theory and Diophantine equations. Mathematics colloquium X-UPS, Palaisau, France, May 11–12, 2005. Palaiseau: Les Éditions de l’École Polytechnique (ISBN 2-7302-1293-0/pbk). 157-185 (2005).
Reviewer: Maurice Mignotte (Strasbourg)
Sums of factorials in binary recurrence sequences. (English) Zbl 0995.11008
Reviewer: Neville Robbins (San Francisco)
On Cohn’s conjecture concerning the Diophantine equation \(x^2+2^m=y^n\). (English) Zbl 1006.11013
Reviewer: Maurice Mignotte (Strasbourg)
MSC:
11D61
Diophantine properties of linear recursive sequences. II. (English) Zbl 0996.11023
Reviewer: Maurice Mignotte (Strasbourg)
Transcendental infinite sums. (English) Zbl 0991.11043
Reviewer: Peter Bundschuh (Köln)
An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II. (English. Russian original) Zbl 1013.11043
Izv. Math. 64, No. 6, 1217-1269 (2000); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, No. 6, 125-180 (2000).
Reviewer: Michel Waldschmidt (Paris)
Proof of the Baker-Feldman theorem via linear forms in two logarithms. (Démonstration du théorème de Baker-Feldman via les formes linéaires en deux logarithmes.) (French) Zbl 1010.11036
Reviewer: Michel Waldschmidt (Paris)
Zero estimates for polynomials in 3 and 4 variables using orbits and stabilisers. (English) Zbl 0986.11047
Denef, Jan (ed.) et al., Hilbert’s tenth problem: relations with arithmetic and algebraic geometry. Proceedings of the workshop, Ghent University, Belgium, November 2-5, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 270, 357-367 (2000).
Reviewer: Maurice Mignotte (Strasbourg)
MSC:
11J86
On general families of parametrized Thue equations. (English) Zbl 0963.11019
Halter-Koch, Franz (ed.) et al., Algebraic number theory and diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30-September 5, 1998. Berlin: Walter de Gruyter. 215-238 (2000).
Reviewer: Istvan Gaál (Debrecen)
Products of factorials in binary recurrence sequences. (English) Zbl 0978.11010
Reviewer: N.Saradha (Mumbai)
Some remarks on questions of diophantine approximation. (Quelques remarques sur des questions d’approximation diophantienne.) (French) Zbl 0927.11040
Reviewer: P.Bundschuh (Köln)
On consecutive integers of the form \(ax^2, by^2\) and \(cz^2\). (English) Zbl 0928.11017
Reviewer: E.L.Cohen (Ottawa)
An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. (English. Russian original) Zbl 0923.11107
Izv. Math. 62, No. 4, 723-772 (1998); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 62, No. 4, 81-136 (1998).
Reviewer: M.Waldschmidt (Paris)
Counting generators of normal integral bases. (English) Zbl 0923.11156
Reviewer: I.Gaál (Debrecen)
Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz. (English) Zbl 0885.11004
Encyclopaedia of Mathematical Sciences 44. Berlin: Springer (ISBN 3-540-61467-2/hbk). 345 p. (1998).
Reviewer: M.Waldschmidt (Paris)
Solving families of simultaneous Pell equations. (English) Zbl 0894.11007
Reviewer: I.Gaál (Debrecen)
Duality on tori and multiplicative dependence relations. (English) Zbl 0886.11035
Reviewer: J.H.Loxton (North Ryde)
Algebraic addition concerning the Siegel theorem on the linearization of holomorphic mapping. (English) Zbl 0873.58057
Reviewer: K.V.Rerikh (Dubna / Russia)
A note on the equation \(ax^ n-by^ n=c\). (English) Zbl 0861.11025
Reviewer: N.Tzanakis (Iraklion)
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