EUDML | Searching for Diophantine quintuples

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Displaying similar documents to “Searching for Diophantine quintuples”

On the Diophantine equation $X^{2} - (2^{2 m} + 1) Y^{4} = - 2^{2 m}$

Michael Stoll, P. G. Walsh, Pingzhi Yuan (2009)

Acta Arithmetica

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Method of infinite ascent applied on $- (2^{p} \cdot A^{6}) + B^{3} = C^{2}$

Susil Kumar Jena (2013)

Communications in Mathematics

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In this paper, the author shows a technique of generating an infinite number of coprime integral solutions for $(A, B, C)$ of the Diophantine equation $- (2^{p} \cdot A^{6}) + B^{3} = C^{2}$ for any positive integral values of $p$ when $p \equiv 1$ (mod 6) or $p \equiv 2$ (mod 6). For doing this, we will be using a published result of this author in The Mathematics Student, a periodical of the Indian Mathematical Society.

A note on the Diophantine equation P(z) = n! + m!

Maciej Gawron (2013)

Colloquium Mathematicae

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We consider the Brocard-Ramanujan type Diophantine equation P(z) = n! + m!, where P is a polynomial with rational coefficients. We show that the ABC Conjecture implies that this equation has only finitely many integer solutions when d ≥ 2 and $P (z) = a_{d} z^{d} + a_{d - 3} z^{d - 3} + \dots + a ₁ x + a ₀$ .

On the Diophantine equation $x^{p} + y^{2 p} = z^{2}$

A. Rotkiewicz, A. Schinzel (1987)

Colloquium Mathematicae

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On the diophantine equation f (x, y) = 0.

H. Kleiman (1976)

Journal für die reine und angewandte Mathematik

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A note on the Diophantine equation $x^{2} + q^{m} = y^{3}$

Hui Lin Zhu (2011)

Acta Arithmetica

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On a Diophantine problem of Bennett

Yang Hai, P. G. Walsh (2010)

Acta Arithmetica

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On a Diophantine equation involving factorials.

Ernst, Bruno (1996)

General Mathematics

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An irregular D(4)-quadruple cannot be extended to a quintuple

Alan Filipin (2009)

Acta Arithmetica

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On simultaneous diophantine equations

Shin-ichi Katayama, Claude Levesque (2003)

Acta Arithmetica

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The diophantine equation $x^{2} + C = y^{n}$ , II

J. H. E. Cohn (2003)

Acta Arithmetica

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A note on the Diophantine equation $(a^{n} x^{m} \pm 1) / (a^{n} x \pm 1) = y^{n} + 1$

Jiagui Luo (2001)

Acta Arithmetica

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On the Diophantine equation $x^{2} + q^{2 m} = 2 y^{p}$

Sz. Tengely (2007)

Acta Arithmetica

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Simultaneous Pell equations

Pingzhi Yuan (2004)

Acta Arithmetica

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Recipes for Solving Diophantine Problems by Baker's Method

W. J. Ellison (1970-1971)

Séminaire de théorie des nombres de Bordeaux

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The Diophantine equation xⁿ = Dy² + 1

J. H. E. Cohn (2003)

Acta Arithmetica

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A note on the diophantine equation a²x⁴ - By² = 1

Jianhua Chen (2001)

Acta Arithmetica

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On some generalizations of the diophantine equation $s (1^{k} + 2^{k} + \dots + x^{k}) + r = d y^{n}$

Csaba Rakaczki (2012)

Acta Arithmetica

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