On a Diophantine equation concerning the number of integer points in special domains. II.

Hajdu, L.

doi:10.5486/pmd.1997.1896

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…Such equations can be handled by a method developed by Stroeker, Tzanakis [36] and independently by Gebel, Pethő, Zimmer [16]. We mention that a similar approach has been used to solve several combinatorial Diophantine equations of different types, for example in [17], [18], [20], [21], [24], [25], [30], [32], [38], [42], [43]. Further, we also solve a particular case of (1) which can be reduced to a genus 2 equation.…”

Section: Proof Of the Theoremsmentioning

confidence: 99%

On $(a,b)$-balancing numbers

Kovàcs¹,

Liptai²,

Olajos³

2010

Publ. Math. Debrecen

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A positive integer n is called a balancing number if 1 + . . . +(n − 1) = (n + 1) + • • • + (n + r) for some positive integer r. Balancing numbers and their generalizations have been investigated by several authors, from many aspects. In this paper we introduce the concept of balancing numbers in arithmetic progressions, and prove several effective finiteness and explicit results about them. In the proofs of our results, among others, we combine Baker's method, the modular method developed by Wiles and others, a result of Bennett about the diophantine equation |ax n − by n | = 1, the Chabauty method and the theory of elliptic curves.

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Section: Proof Of the Theoremsmentioning

confidence: 99%

On $(a,b)$-balancing numbers

Kovàcs¹,

Liptai²,

Olajos³

2010

Publ. Math. Debrecen

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30 years of collaboration

Fuchs

Hajdu

2016

Period Math Hung

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Abstract. We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem), which will be presented in turn.

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Taming Genus 0 (or 1) Components on Variables-Separated Equations

Fried

2023

Albanian J. Math.

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On a Diophantine equation concerning the number of integer points in special domains. II.

Cited by 3 publications

References 7 publications

On $(a,b)$-balancing numbers

On $(a,b)$-balancing numbers

30 years of collaboration

Taming Genus 0 (or 1) Components on Variables-Separated Equations

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