Found 1,000 Documents (Results 1–100)
Lecture notes on Diophantine analysis. With an appendix by Francesco Amoroso. 2nd edition. (English) Zbl 07903163
EMS Series of Lectures in Mathematics 36. Berlin: European Mathematical Society (EMS) (ISBN 978-3-98547-077-8/pbk; 978-3-98547-577-3/ebook). xii, 399 p. (2024).
Reviewer: István Gaál (Debrecen)
On the solutions of the Lucas sequence equation \(\pm\frac{1}{V_n(P_2, Q_2)} = \sum_{k=1}^\infty\frac{U_{k-1}(P_1,Q_1)}{x^k}\). (English) Zbl 1543.11019
The divisibility of the class number of the imaginary quadratic fields \(\mathbb{Q}(\sqrt{1-2m^k})\). (English) Zbl 07887403
On the \(x\)-coordinates of Pell equations that are products of two Pell numbers. (English) Zbl 07859869
Reviewer: Ingrid Vukusic (Salzburg)
Some exponential Diophantine equations. III: A new look at the generalized Lebesgue-Nagell equation. (English) Zbl 07837711
Reviewer: Roberto Amato (Messina)
Bounds for the smallest integral solution of Pell equation over a number field. (English) Zbl 07836765
Reviewer: Mahadi Ddamulira (Kampala)
On the \(X\)-coordinates of Pell equations \(X^2 - dY^2 = \pm 1\) as difference of two Fibonacci numbers. (English) Zbl 1540.11012
Reviewer: Mahadi Ddamulira (Kampala)
A structure theorem for the restricted sum of four squares. (English) Zbl 1543.11042
Reviewer: Meinhard Peters (Münster)
MSC:
11E25
Squares in recurrences using elliptic curves. (English) Zbl 1543.11052
Reviewer: Maciej Ulas (Kraków)
Specializations of a generic rank-2 curve of Shioda. (English) Zbl 1540.11064
Reviewer: Mentzelos Melistas (Enschede)
Counting integer points on affine surfaces with a side condition. arXiv:2408.11453
Preprint, arXiv:2408.11453 [math.NT] (2024).
On the integer solutions of the Diophantine equation \((x+y+z)^2=xyw\). (English) Zbl 1539.11055
MSC:
11D09
On simultaneous Pell equations \(x^2-(m^2-1) y^2=z^2-(n^2-1) y^2=1\). (Chinese. English summary) Zbl 07828134
On parametric and matrix solutions to the Diophantine equation \(x^2 + d y^2- z^2=0\) where \(d\) is a positive square-free integer. (English) Zbl 07826521
Reviewer: {}
MSC:
11D09
A note on Dujella’s unicity conjecture. (English) Zbl 1539.11056
Reviewer: Ingrid Vukusic (Salzburg)
Similarity for matrices obtained by clockwise “rotation”. (English) Zbl 07794422
Reviewer: Józef Drewniak (Rzeszów)
Integer solution analysis for a Diophantine equation with exponentials. (English) Zbl 1538.11088
MSC:
11D09
Some multi figurate numbers in terms of generalized Fibonacci and Lucas numbers. (English) Zbl 1538.11042
Existence of the solutions to the Brocard-Ramanujan problem for norm forms. (English) Zbl 1533.11068
Reviewer: Lajos Hajdu (Debrecen)
A tale of two by two matrices. (English) Zbl 1533.11067
Reviewer: Franz Lemmermeyer (Jagstzell)
Negative Pell equation and stationary configurations of point vortices on the plane. (English. Russian original) Zbl 07761802
Math. Notes 114, No. 1, 46-54 (2023); translation from Mat. Zametki 114, No. 1, 57-67 (2023).
Reviewer: Fatma Gamze Düzgün (Ankara)
Class number one problem for a non-Richaud-Degert type family of real quadratic fields. (English) Zbl 1538.11186
Refined spectral properties of Dirichlet and Neumann problems for the Laplace operator in a rectangular domain. (Russian. English summary) Zbl 1538.35233
\(k\)-Fibonacci numbers which are Padovan or Perrin numbers. (English) Zbl 1534.11024
Reviewer: Mahadi Ddamulira (Kampala)
Jeśmanowicz’ conjecture for non-primitive Pythagorean triples. (English) Zbl 1538.11091
Reviewer: Nikos Tzanakis (Iraklion)
Ambiguous solutions of a Pell equation. (English) Zbl 1533.11066
Reviewer: Yasutsugu Fujita (Narashino)
MSC:
11D09
Calkin-Wilf sequences for irrational numbers. (English) Zbl 1518.11021
Reviewer: Symon Serbenyuk (Kyïv)
On the \(X\)-coordinates of Pell equations of the form \(px^2\). (English) Zbl 1538.11044
Reviewer: István Gaál (Debrecen)
On two Olympiad exercises. A walk in number theory. (À propos de deux exercices d’olympiades. Petite promenade en théorie des nombres.) (French. English summary) Zbl 1527.11025
Reviewer: Franz Lemmermeyer (Jagstzell)
MSC:
11D09
Self generating of Diophantine equation \(d^2-c^2=b^2-a^2\) and \(N\)-tuples. (English) Zbl 1520.11039
MSC:
11D09
Odds inversion problem with replacement. (English) Zbl 1520.11038
MSC:
11D09
The order of the fundamental solution of \(x^2 -Dy^2 =1\) in \(\mathbb{Z}[\sqrt{D}]/\langle D \rangle\). (English) Zbl 1501.11044
MSC:
11D09
Matrix morphology and composition of higher degree forms with applications to Diophantine equations. (English) Zbl 1497.11096
Lattice equable qadrilaterals. II: Kites, trapezoids and cyclic quadrilaterals. (English) Zbl 1513.51065
Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences. (English) Zbl 1497.11069
Reviewer: Mahadi Ddamulira (Kampala)
Terms of recurrence sequences in the solution sets of generalized Pell equations. (English) Zbl 1501.11045
Reviewer: Clemens Fuchs (Salzburg)
On the number of monogenizations of a quartic order (with an appendix by Shabnam Akhtari). (English) Zbl 1499.11328
Reviewer: István Gaál (Debrecen)
Closed formulae for certain Fermat-Pell equations. (English) Zbl 1493.11161
Reviewer: Anitha Srinivasan (Madrid)
Some exponential Diophantine equations. II: The equation \(x^2 - dy^2=k^z\) for even \(k\). (English) Zbl 1491.11034
MSC:
11D61
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).
On the representation of integers by binary forms defined by means of the relation \((x + yi)^n= R_n(x,y) + J_n(x,y)i\). (English) Zbl 1491.11040
Reviewer: István Gaál (Debrecen)
Singular matrices that are products of two idempotents or products of two nilpotents. (English) Zbl 1485.15037
Reviewer: Laura Cossu (Padova)
The matrix equation \(aX^m+bY^n=cI\) over \(M_2(\mathbb{Z})\). arXiv:2212.14139
Preprint, arXiv:2212.14139 [math.NT] (2022).
Solving Diophantine equations using factorization in number fields. (Czech) Zbl 1538.11101
Reviewer: Jaroslav Hančl (Ostrava)
Continued fractions with prescribed period. (Czech) Zbl 1538.11022
Reviewer: Štěpán Holub (Praha)
New curiosity bivariate quadratic quaternionic polynomials and their roots. (English) Zbl 1524.11206
On \(t\)-balancers, \(t\)-balancing numbers and Lucas \(t\)-balancing numbers. (English) Zbl 1518.11015
On the integral solutions of binary quadratic Diophantine equation \(ax^2-bx=cy^2\). (English) Zbl 1499.11163
MSC:
11D09
On the solutions of the Pell-type equation \(x^2-ry^2=r\) in the ring of Gaussian integers \(\mathbb{Z}[i]\) with \(r\) a Gaussian prime. (English) Zbl 1499.11161
On the finiteness of solutions for polynomial-factorial Diophantine equations. (English) Zbl 1492.11082
Reviewer: Maciej Ulas (Kraków)
The Diophantine equation \(X^3=u+v\) over real quadratic fields. II. (English) Zbl 1501.11046
Reviewer: István Gaál (Debrecen)
MSC:
11D25
Pellian equations of special type. (English) Zbl 1497.11070
Reviewer: Mahadi Ddamulira (Kampala)
Thue’s equation as a tool to solve two different problems. (English) Zbl 1481.11034
Reviewer: István Gaál (Debrecen)
On the Diophantine equation \(x^3\pm 1=7qy^2\). (Chinese. English summary) Zbl 1488.11082
MSC:
11D25
Smooth values of quadratic polynomials. (English) Zbl 1487.11085
Reviewer: Andrej Dujella (Zagreb)
How to calculate the proportion of everywhere locally soluble diagonal hypersurfaces. (English) Zbl 1492.14038
Reviewer: Arman Shamsi Zargar (Ardabil)
\(D(-1)\) tuples in imaginary quadratic fields. (English) Zbl 1488.11077
Reviewer: Dimitros Poulakis (Thessaloniki)
Corrigendum to: “On two classes of simultaneous Pell equations with no solutions”. (English) Zbl 1464.11034
MSC:
11D09
Chebyshev polynomials and Pell equations over finite fields. (English) Zbl 07361081
Reviewer: Andrej Dujella (Zagreb)
Dilogarithm identities for solutions to Pell’s equation in terms of continued fraction convergents. (English) Zbl 1483.11050
On the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial. (Russian. English summary) Zbl 1482.11040
MSC:
11D09
Integral unicyclic graphs. (English) Zbl 1459.05162
Symmetry-based approach to the problem of a perfect cuboid. (English. Russian original) Zbl 1483.11059
J. Math. Sci., New York 252, No. 2, 266-282 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 152, 143-158 (2018).
Pythagorean Triples in the Fibonacci Model Set. arXiv:2109.03440
Preprint, arXiv:2109.03440 [math.DS] (2021).
Proof of the Tijdeman-Zagier Conjecture via Slope Irrationality and Term Coprimality. arXiv:2103.02431
Preprint, arXiv:2103.02431 [math.NT] (2021).
On a conjecture concerning the generalized Ramanujan-Nagell equation. (English) Zbl 1501.11050
Reviewer: Gökhan Soydan (Bursa)
On the common solution of the simultaneous Diophantine equations \({x^2} - 18{y^2} = 1\) and \({y^2} - b z^2 = 16\). (Chinese. English summary) Zbl 1474.11082
MSC:
11D09
A note on the use of Rédei polynomials for solving the polynomial Pell equation and its generalization to higher degrees. (English) Zbl 1481.11031
Reviewer: Paul Voutier (London)
Markoff equation with Pell components. (English) Zbl 1468.11090
Reviewer: Olaf Ninnemann (Uffing am Staffelsee)
The Markoff-Fibonacci numbers. (English) Zbl 1473.11042
Reviewer: Florian Luca (Johannesburg)
Uniqueness for sums of nonvanishing squares. (English) Zbl 1471.11131
Reviewer: Mowaffaq Hajja (Amman)
MSC:
11E25
On certain \(D(9)\) and \(D(64)\) Diophantine triples. (English) Zbl 1474.11079
Reviewer: Florian Luca (Johannesburg)
On the equation \(y^2=x^6+k\). (English) Zbl 1466.14027
Reviewer: B. Z. Moroz (Bonn)
On the solutions of the simultaneous Diophantine equations \({x^2} - 14{y^2} = 1\) and \({y^2} - d{z^2} = 16\). (Chinese. English summary) Zbl 1463.11101
MSC:
11D09
Extension of the Stormer theorem. (Chinese. English summary) Zbl 1463.11100
MSC:
11D09
On the common solutions of Pell equations \({x^2} - ({c^2} - 1){y^2} = {y^2} - 2{p_1}{p_2}{p_3}{z^2} = 1\). (Chinese. English summary) Zbl 1463.11099
MSC:
11D09
Can a Lucas number be a sum of three repdigits? (English) Zbl 1524.11027
Reviewer: Takao Komatsu (Hangzhou)
Effective simultaneous rational approximation to pairs of real quadratic numbers. (English) Zbl 1455.11095
Reviewer: István Gaál (Debrecen)
The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. (English) Zbl 1471.11065
On the Diophantine equation \(x^2-2y^4=M (M=17, 41, 73, 89, 97)\). (Chinese. English summary) Zbl 1463.11103
MSC:
11D25
A class of Diophantine equation. (Chinese. English summary) Zbl 1463.11098
MSC:
11D09
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