Found 4,158 Documents (Results 1–100)
On the Diophantine equation \(a^x+(a+5b)^y=z^2\). (English) Zbl 07907961
MSC:
11D61
Mersenne numbers that are expressible as the summation of two Fibonacci numbers. (English) Zbl 07928026
Equal sums of two cubes of quadratic forms. (English) Zbl 07924592
Andrews, George E. (ed.) et al., Analytic and combinatorial number theory: the legacy of Ramanujan. Contributions in honor of Bruce C. Berndt. Selected papers based on the presentations at the conference, Champaign, IL, USA, June 6–9, 2019. Singapore: World Scientific. Monogr. Number Theory 12, 583-608 (2024).
The congruence equation \(\bar{a} + \bar{b} \equiv \bar{c} \pmod p\). (English) Zbl 07924565
Andrews, George E. (ed.) et al., Analytic and combinatorial number theory: the legacy of Ramanujan. Contributions in honor of Bruce C. Berndt. Selected papers based on the presentations at the conference, Champaign, IL, USA, June 6–9, 2019. Singapore: World Scientific. Monogr. Number Theory 12, 107-118 (2024).
On the solutions of \(x^2 = By^p + Cz^p\) and \(2x^2 = By^p + Cz^p\) over totally real fields. (English) Zbl 07920317
Power values of power sums: a survey. (English) Zbl 07919515
Abdellatif, Ramla (ed.) et al., Women in numbers Europe IV. Research directions in number theory. Selected papers based on the presentations at the 4th workshop, WINE 4, Utrecht, the Netherlands, August 29 – September 2, 2022. Cham: Springer. Assoc. Women Math. Ser. 32, 155-193 (2024).
On the Diophantine equations \(q^x + p(2q + 1)^y = z^2\) and \(q^x + p(4q + 1)^y = z^2\). (English) Zbl 07916021
MSC:
11D61
On equations \((-1)^\alpha p^x+ (-1)^\beta (2^k(2p + 1))^y= z^2\) with Sophie Germain prime \(p\). (English) Zbl 07904869
Cobalancing hybrid numbers. (English) Zbl 07904196
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 07894873
On integral graphs which belong to the class \(\overline{\alpha K_{a, a, a}\cup \beta K_{b, b, b}}\). (English) Zbl 07892720
MSC:
05C50
The divisibility of the class number of the imaginary quadratic fields \(\mathbb{Q}(\sqrt{1-2m^k})\). (English) Zbl 07887403
Some results concerning the exponential Diophantine equation \((a^n-1)(b^m-1) = x^2\). (English) Zbl 07881005
On a class of Lebesgue-Ramanujan-Nagell equations. (English) Zbl 07880178
Reviewer: Andrzej Dąbrowski (Szczecin)
Translations and extensions of the Nicomachean identity. (English) Zbl 07875570
Reviewer: Takao Komatsu (Hangzhou)
Minimization of hypersurfaces. (English) Zbl 07872166
On perfect powers that are sums of cubes of a nine term arithmetic progression. (English) Zbl 07869080
On the classification and dispersability of circulant graphs with two jump lengths. (English) Zbl 1541.05124
On sums of two Fibonacci numbers that are powers of numbers with limited Hamming weight. (English) Zbl 07868213
Reviewer: Florian Luca (Johannesburg)
Unsolvability of two diophantine equations of the form \(p^a+(p-1)^b=c^2\). (English) Zbl 07866760
MSC:
11D61
Cullen numbers and Woodall numbers in generalized Fibonacci sequences. (English) Zbl 07865940
Reviewer: Mahadi Ddamulira (Kampala)
On the \(x\)-coordinates of Pell equations that are products of two Pell numbers. (English) Zbl 07859869
Reviewer: Ingrid Vukusic (Salzburg)
Primes of the form \(X^3 + NY^3\) and a family of non-singular plane curves which violate the local-global principle. (English) Zbl 07859697
Reviewer: Matteo Verzobio (Pisa)
Newton polygons and the constant associated with the Prouhet-Tarry-Escott problem. (English) Zbl 07856589
The solutions of the Diophantine equations \(p^x+p^y=z^q\) and \(p^x-p^y=z^q\). (English) Zbl 07846035
MSC:
11D61
On the square of Fibonacci and Lucas numbers of the form \((2^{2s}-1)^x+(2^{s+1})^y\). (English) Zbl 07846028
Decomposable forms generated by linear recurrences. (English) Zbl 07842618
Reviewer: Clemens Fuchs (Salzburg)
A Diophantine equation with powers of three consecutive \(k\)-Fibonacci numbers. (English) Zbl 1539.11033
Reviewer: Mahadi Ddamulira (Kampala)
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)
Controllability of networked multiagent systems based on linearized Turing’s model. (English) Zbl 1536.93083
How to solve a binary cubic equation in integers. (English) Zbl 1542.11038
Reviewer: Dimitros Poulakis (Thessaloniki)
Number of solutions to a special type of unit equations in two unknowns. (English) Zbl 1542.11041
Reviewer: Florian Luca (Johannesburg)
An elementary approach to the generalized Ramanujan-Nagell equation. (English) Zbl 07833746
Reviewer: Ingrid Vukusic (Salzburg)
MSC:
11D61
On the Diophantine equation \(x^2 + C = y^n\). (English) Zbl 1540.11024
Reviewer: Seyran S. İbrahimov (Famagusta)
On perfect powers that are sum of two balancing numbers. (English) Zbl 07829377
Reviewer: Takao Komatsu (Hangzhou)
MSC:
11B37
A note on the Diophantine equations \(2ln^2 = 1 + q + \cdots + q^\alpha\) and application to odd perfect numbers. (English) Zbl 07827032
Reverse engineered Diophantine equations over \(\mathbb{Q}\). (English. French summary) Zbl 07824612
Infinite families of solutions for \(A^3 + B^3 = C^3 + D^3\) and \(A^4 + B^4 + C^4 + D^4 + E^4 = F^4\). (English) Zbl 1541.11031
Reviewer: Yong Zhang (Changsha)
MSC:
11D25
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)
On the braid group action on exceptional sequences for weighted projective lines. (English) Zbl 07815080
A structure theorem for the restricted sum of four squares. (English) Zbl 07814070
Reviewer: Meinhard Peters (Münster)
MSC:
11E25
Quartic integral polynomial Pell equations. (English) Zbl 1540.11020
Reviewer: Nikos Tzanakis (Iraklion)
Terms of recurrence sequences in the solution sets of norm form equations. (English) Zbl 1539.11029
Reviewer: Clemens Fuchs (Salzburg)
Common terms of Leonardo and Jacobsthal numbers. (English) Zbl 07797022
Reviewer: Mahadi Ddamulira (Kampala)
On the \(abc\) conjecture in algebraic number fields. (English) Zbl 07796300
Reviewer: Günter Lettl (Graz)
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)
Squares in recurrences using elliptic curves. (English) Zbl 07785377
Reviewer: Maciej Ulas (Kraków)
On the Diophantine equations \((p+a)^x-p^y=z^2\) and \(p^x-(p+a)^y=z^2\). (English) Zbl 1538.11112
MSC:
11D61
On the Diophantine equation \(a^x+(a+2)^y=z^2\) where \(a\) is congruent to 19 modulo 28. (English) Zbl 1538.11116
MSC:
11D61
On the Diophantine equation \(147^x+741^y=z^2\). (English) Zbl 1538.11117
MSC:
11D61
On the positive integer solutions of \(p^x+p^y=z^2\) in the Fibonacci and Lucas numbers, where \(p\) is prime. (English) Zbl 1538.11111
On the Diophantine equation \(\frac{1}{a}+\frac{1}{b}=\frac{m}{pq}\). (English) Zbl 1538.11120
MSC:
11D68
Specializations of a generic rank-2 curve of Shioda. (English) Zbl 1540.11064
Reviewer: Mentzelos Melistas (Enschede)
Bounds on the exceptional set in the \(abc\) conjecture. arXiv:2410.12234
Preprint, arXiv:2410.12234 [math.NT] (2024).
Counting integer points on affine surfaces with a side condition. arXiv:2408.11453
Preprint, arXiv:2408.11453 [math.NT] (2024).
An Exponential Diophantine equation \(x^2+3^{\alpha} 113^{\beta}=y^{\mathfrak{n}}\). arXiv:2405.09252
Preprint, arXiv:2405.09252 [math.NT] (2024).
Asymptotic Fermat’s Last Theorem for a family of equations of signature \((2, 2n, n)\). arXiv:2404.14098
Preprint, arXiv:2404.14098 [math.NT] (2024).
WITHDRAWN: Solution of the Diophantine equation \(x^2 + p^k=y^n\). arXiv:2402.19445
Preprint, arXiv:2402.19445 [math.NT] (2024); retraction notice ibid.
Linear Diophantine equation (LDE) decoder: a training-free decoding algorithm for multifrequency SSVEP with reduced computation cost. (English) Zbl 07892380
MSC:
93-XX
On the integer solutions of the Diophantine equation \((x+y+z)^2=xyw\). (English) Zbl 1539.11055
MSC:
11D09
On the non-linear Diophantine equations \(4^x - a^y = dz^2\) and \(4^x + a^y = dz^2\). (English) Zbl 07829209
MSC:
11D61
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
On perfect powers in \(k\)-generalized Pell-Lucas sequence. (English) Zbl 1542.11027
Reviewer: Mahadi Ddamulira (Kampala)
A note on Dujella’s unicity conjecture. (English) Zbl 1539.11056
Reviewer: Ingrid Vukusic (Salzburg)
On the Tarry-Escott and related problems for \(2 \times 2\) matrices over \(\mathbb{Q}\). (English) Zbl 1539.11064
Reviewer: Hayder Hashim (Kufa)
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