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

Susil Kumar Jena

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

Searching for Diophantine quintuples

Mihai Cipu, Tim Trudgian (2016)

Acta Arithmetica

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We consider Diophantine quintuples a, b, c, d, e. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441 \cdot 10^{26}$ Diophantine quintuples.

A note on the number of $S$ -Diophantine quadruples

Florian Luca, Volker Ziegler (2014)

Communications in Mathematics

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Let $(a_{1}, \dots, a_{m})$ be an $m$ -tuple of positive, pairwise distinct integers. If for all $1 \leq i < j \leq m$ the prime divisors of $a_{i} a_{j} + 1$ come from the same fixed set $S$ , then we call the $m$ -tuple $S$ -Diophantine. In this note we estimate the number of $S$ -Diophantine quadruples in terms of $| S | = r$ .

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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The Diophantine equation $x^{2} + c = y^{n}$ : a brief overview.

Muriefah, Fadwa S.Abu, Bugeaud, Yann (2006)

Revista Colombiana de Matemáticas

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On a Diophantine equation.

Acu, Dumitru (2007)

General Mathematics

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

H. Kleiman (1976)

Journal für die reine und angewandte Mathematik

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On a Diophantine problem of Bennett

Yang Hai, P. G. Walsh (2010)

Acta Arithmetica

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On simultaneous diophantine equations

Shin-ichi Katayama, Claude Levesque (2003)

Acta Arithmetica

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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 $P (z) = a_{d} z^{d} + a_{d - 3} z^{d - 3} + \dots + a ₁ x + a ₀$ .

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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A note on the diophantine equation a²x⁴ - By² = 1

Jianhua Chen (2001)

Acta Arithmetica

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On the Diophantine equation (x² ± C)(y² ± D) = z⁴

Pingzhi Yuan, Jiagui Luo (2010)

Acta Arithmetica

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Displaying similar documents to “Method of infinite ascent applied on - ( 2 p · A 6 ) + B 3 = C 2 ”

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