Almost powers in the Lucas sequence

Yann Bugeaud; Florian Luca; Maurice Mignotte; Samir Siksek

Displaying similar documents to “Almost powers in the Lucas sequence”

On $D$ so that $x^{2} - D y^{2} = \pm m$ .

Robertson, John P. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Generators for the elliptic curve $y^{2} = x^{3} - n x$

Yasutsugu Fujita, Nobuhiro Terai (2011)

Journal de Théorie des Nombres de Bordeaux

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Let $E$ be an elliptic curve given by $y^{2} = x^{3} - n x$ with a positive integer $n$ . Duquesne in 2007 showed that if $n = (2 k^{2} - 2 k + 1) (18 k^{2} + 30 k + 17)$ is square-free with an integer $k$ , then certain two rational points of infinite order can always be in a system of generators for the Mordell-Weil group of $E$ . In this paper, we generalize this result and show that the same is true for infinitely many binary forms $n = n (k, l)$ in $ℤ [k, l]$ .

On $D$ sot hat $x^{2} - D y^{2}$ represents $m$ and $- m$ and not $- 1$ .

Robertson, John P. (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Rational approximations to $\sqrt[3]{2}$ and other algebraic numbers revisited

Paul M. Voutier (2007)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we establish improved effective irrationality measures for certain numbers of the form $\sqrt[3]{n}$ , using approximations obtained from hypergeometric functions. These results are very close to the best possible using this method. We are able to obtain these results by determining very precise arithmetic information about the denominators of the coefficients of these hypergeometric functions. Improved bounds for the Chebyshev functions in arithmetic progressions $θ (k, l; x)$ and...

On the parity of generalized partition functions, III

Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)

Journal de Théorie des Nombres de Bordeaux

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Improving on some results of J.-L. Nicolas [], the elements of the set $𝒜 = 𝒜 (1 + z + z^{3} + z^{4} + z^{5})$ , for which the partition function $p (𝒜, n)$ (i.e. the number of partitions of $n$ with parts in $𝒜$ ) is even for all $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

The composition of the gcd and certain arithmetic functions.

Bordellès, Olivier (2010)

Journal of Integer Sequences [electronic only]

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Displaying similar documents to “Almost powers in the Lucas sequence”

On D so that x 2 - D y 2 = ± m .

Generators for the elliptic curve y 2 = x 3 - n x

On D sot hat x 2 - D y 2 represents m and - m and not - 1 .

Rational approximations to 2 3 and other algebraic numbers revisited

On the parity of generalized partition functions, III

The composition of the gcd and certain arithmetic functions.

On $D$ so that $x^{2} - D y^{2} = \pm m$ .

Generators for the elliptic curve $y^{2} = x^{3} - n x$

On $D$ sot hat $x^{2} - D y^{2}$ represents $m$ and $- m$ and not $- 1$ .

Rational approximations to $\sqrt[3]{2}$ and other algebraic numbers revisited