Finding integers k for which a given Diophantine equation has no solution in kth powers of integers

Andrew Granville

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Displaying similar documents to “Finding integers k for which a given Diophantine equation has no solution in kth powers of integers”

Variants of the Brocard-Ramanujan equation

Omar Kihel, Florian Luca (2008)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we discuss variations on the Brocard-Ramanujan Diophantine equation.

On the family of diophantine triples ${k + 2, 4 k, 9 k + 6}$ .

Filipin, Alan, Togbé, Alain (2009)

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

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On the positive integral solutions of the Diophantine equation $x^{3} + b y + 1 - x y z = 0$ .

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On the Diophantine equations of type $a^{x} + b^{y} = c^{z}$ .

Acu, Dumitru (2005)

General Mathematics

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On rough and smooth neighbors.

William D. Banks, Florian Luca, Igor E. Shparlinski (2007)

Revista Matemática Complutense

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We study the behavior of the arithmetic functions defined by F(n) = P⁺(n) / P^-(n+1) and G(n) = P⁺(n+1) / P^-(n) (n ≥ 1) where P⁺(k) and P^-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.

Practical Aurifeuillian factorization

Bill Allombert, Karim Belabas (2008)

Journal de Théorie des Nombres de Bordeaux

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We describe a simple procedure to find Aurifeuillian factors of values of cyclotomic polynomials $Φ_{d} (a)$ for integers $a$ and $d > 0$ . Assuming a suitable Riemann Hypothesis, the algorithm runs in deterministic time $\tilde{O} (d^{2} L)$ , using $O (d L)$ space, where $L ≔ log (|a| + 1)$ .

When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently

Claudia A. Spiro-Silverman (1992)

Acta Arithmetica

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On systems of composite Lehmer numbers with prime indices

J. Wójcik (1996)

Colloquium Mathematicae

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