Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation
From MaRDI portal
Publication:3379047
DOI10.1112/S0010437X05001739zbMath1128.11013arXivmath/0405220WikidataQ56813320 ScholiaQ56813320MaRDI QIDQ3379047
Samir Siksek, Maurice Mignotte, Yann Bugeaud
Publication date: 6 April 2006
Published in: Compositio Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0405220
Thue-Mahler equations (11D59) Computer solution of Diophantine equations (11Y50) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)
Related Items
ON THE DIOPHANTINE EQUATIONx2+d2l+ 1=yn, On a family of Thue equations of degree 16, Variations of Lehmer's conjecture for Ramanujan's tau-function, Differences between perfect powers: The Lebesgue-Nagell equation, On the Ramanujan-Nagell type Diophantine equation x2+Akn=B, An upper bound for solutions of the Lebesgue-Nagell equation \(x^2+a^2=y^n\), On the Diophantine equation \(x^2+5^a\cdot 11^b=y^n\), On the equation x2 + dy6 = zp for square-free 1 ≤ d ≤ 20, Variants of Lehmer's speculation for newforms, Reverse engineered Diophantine equations over \(\mathbb{Q}\), On some generalized Lebesgue-Nagell equations, Differences between perfect powers: prime power gaps, AN APPLICATION OF THE MODULAR METHOD AND THE SYMPLECTIC ARGUMENT TO A LEBESGUE–NAGELL EQUATION, Reverse engineered Diophantine equations, A modular approach to cubic Thue-Mahler equations, A multi-Frey approach to Fermat equations of signature $(r,r,p)$, On the Diophantine equation \(x^2+3^a41^b=y^n\), On the Diophantine Equation x 2 + 2 α 5 β 13 γ = y n, On Lebesgue–Ramanujan–Nagell Type Equations, There is no Diophantine quintuple, On the solutions of certain Lebesgue-Ramanujan-Nagell equations, THE ADDITIVE S-UNIT STRUCTURE OF QUADRATIC FIELDS, The diophantine equation x2 + paqb = yq, Unnamed Item, Perfect powers from products of terms in Lucas sequences, On \(px^{2}+q^{2n}=y^{p}\) and related Diophantine equations, Solutions of some generalized Ramanujan-Nagell equations, ON THE DIOPHANTINE EQUATION x2 + 5a 13b = yn, Hyperelliptic curves and newform coefficients, Perfect powers expressible as sums of two cubes, Products of members of Lucas sequences with indices in an interval being a power, On the Diophantine equation \(1 + 2^a + x^b = y^n\), A Lucas-Lehmer approach to generalised Lebesgue-Ramanujan-Nagell equations, ON THE DIOPHANTINE EQUATION x2 + 2a · 5b = yn, Effective results for linear equations in members of two recurrence sequences, A GENERALIZATION OF THE RAMANUJAN–NAGELL EQUATION, Almost powers in the Lucas sequence, ON THE DIOPHANTINE EQUATION x2 + C = 2yn, ON THE FACTORISATION OF, Diophantine equations after Fermat's last theorem, The equation $(x-d)^5+x^5+(x+d)^5=y^n$, On the Diophantine equation \(x^2+5^m=y^n\), On the Diophantine equation \(x^2+D^m=p^n\), Unnamed Item, On the diophantine equation x2+5a·pb=yn, SOLUTIONS TO A LEBESGUE–NAGELL EQUATION, Unnamed Item
Uses Software