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On Lebesgue–Ramanujan–Nagell Type Equations (Q3298293)

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Language	Label	Description	Also known as
English	On Lebesgue–Ramanujan–Nagell Type Equations	scientific article

Statements

scholarly article

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On Lebesgue–Ramanujan–Nagell Type Equations (English)

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Class Groups of Number Fields and Related Topics

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publication date

14 July 2020

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zbMATH Keywords

Diophantine equations

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Ramanujan-Nagell

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-981-15-1514-9_14

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On the diophantine equation \(x^ 2+2^ k=y^ n\)

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The diophantine equation \(x^2+3^m=y^n\)

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On the Diophantine equation \(x^2+2^k=y^n\). II

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On the Diophantine equation \(x^2+q^{2k+1}=y^n\)

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On the diophantine equation ax<sup>2</sup>+b<sup>m</sup>=4y<sup>n</sup>

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ON THE DIOPHANTINE EQUATION x2 + 52k = yn

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Ternary Diophantine Equations via Galois Representations and Modular Forms

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On the Diophantine equation \(x^2 + p^{2k} = y^n\)

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ON THE DIOPHANTINE EQUATION<i>x</i><sup>2</sup>+<i>d</i><sup>2<i>l</i>+ 1</sup>=<i>y<sup>n</sup></i>

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On the generalized Ramanujan-Nagell equation I

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On the generalized Ramanujan-Nagell equation, II

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On the solutions of a Lebesgue-Nagell type equation

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Existence of primitive divisors of Lucas and Lehmer numbers

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On Le's and Bugeaud's papers about the equation \(ax^2 + b^{2m-1} = 4c^p\)

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A Note on Diophantine Equation Y 2 + k = X 5

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On the diophantine equation $x^2 - p^m = ±y^n$

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On some exponential Diophantine equations

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Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation

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On the diophantine equation x 2 + 2a · 3b · 11c = y n

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On the Diophantine equation \(x^2+5^a\cdot 11^b=y^n\)

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On the Diophantine Equation X2+19M=YN

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Divisibility of the class numbers of imaginary quadratic fields

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Class groups of imaginary quadratic fields of $3$-rank at least $2$

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The Diophantine Equation 2 n+2 - 7 = x 2 and Related Problems

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The diophantine equation \(x^ 2 + 2^ k = y^ n\)

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The diophantine equation x² + C = yⁿ

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Perfect Pell Powers

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The Diophantine equation \(x^2+2^k=y^n\). II

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On the Diophantine equation <i>x</i> <sup>2</sup> + <i>C</i>= <i>y<sup>n</sup> </i> for <i>C</i> = 2<sup> <i>a</i> </sup>3<sup> <i>b</i> </sup>17<sup> <i>c</i> </sup> and <i>C</i> = 2<sup> <i>a</i> </sup>13<sup> <i>b</i> </sup>17<sup> <i>c</i> </sup>

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On the divisibility of class numbers of quadratic fields and the solvability of Diophantine equations

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Divisibility of class numbers of certain families of quadratic fields

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Complete solution of the diophantine equation \(X^ 2+1=dY^ 4\) and a related family of quartic Thue equations

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On the diophantine equation \(x^ 2+D=4p^ n\)

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On the Diophantine Equations d 1 x 2 + 2 2m d 2 = y n and d 1 x 2 + d 2 = 4y n

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On the diophantine equation \(D_ 1 x^ 2+ D^ m_ 2= 4y^ n\)

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A note on the number of solutions of the generalized Ramanujan-Nagell equation \(D_ 1x^ 2+D_ 2=4p^ n\)

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On Cohn's conjecture concerning the Diophantine equation \(x^2+2^m=y^n\)

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On some generalized Lebesgue-Nagell equations

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Difference between powers and squares of integers

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On the Diophantine equation \(x^2+5^m=y^n\)

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On the diophantine equation \(x^2+D=4y^q\)

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New theorems concerning the diophantine equation $x^2 + D =4y^q$

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On an diophantine equation

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On the equation \(x^2 + 2^a \cdot 3^b = y^n\)

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On the diophantine equations <i>x</i><sup>2</sup> + 74 = <i>y</i><sup>5</sup> and <i>x</i><sup>2</sup> + 86 = <i>y</i><sup>5</sup>

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On a diophantine equation

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The diophantine equation \(x^2+5^{2k+1}= y^n\)

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ON THE DIOPHANTINE EQUATION x<sup>2</sup> + C = 2y<sup>n</sup>

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Verallgemeinerung eines Fermatschen Satzes

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On a diophantine equation in two unknowns

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Solutions of some generalized Ramanujan-Nagell equations

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On the Diophantine equation x<sup>2</sup>+7=y<sup>m</sup>

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On the Diophantine equation \(x^2= y^p+2^kz^p\)

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The Diophantine Equation x^{2}+11^{m}=y^{n}

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On the Diophantine equation x^2+7^{alpha}.11^{beta}=y^n

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On the Diophantine equation \(x^2 + 2^a \cdot 19^b = y^n\)

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A note on the Diophantine equations $x^{2}\pm5^{\alpha}\cdot p^{n}=y^{n}$

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Simplifying the solution of Ljunggren's equation \(x^ 2+1=2y^ 4\)

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Die Anzahl von Lösungen gewisser diophantischer Gleichungen

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On the Diophantine equation \(x^2+2=y^n\)

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On the Diophantine equation \(x^ 2+a^ 2=2y^ p\).

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On the Diophantine equation x<sup>2</sup>+q<sup>2m</sup>=2y<sup>p</sup>

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A note on the Diophantine equation x<sup>2</sup>+q<sup>m</sup>=y<sup>3</sup>

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ON THE EXPONENTIAL DIOPHANTINE EQUATION<i>x</i><sup>2</sup>+<i>p</i><sup>2<i>m</i></sup>=2<i>y</i><sup><i>n</i></sup>

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Identifiers

zbMATH Open document ID

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10.1007/978-981-15-1514-9_14

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3298293

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