On the integer solutions of exponential equations in function fields

Zannier, Umberto

doi:10.5802/aif.2036

Cited by 16 publications

(37 citation statements)

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“…Then there is an effectively computable constant C such 15 Instead of trying to review the huge related literature, we only refer to the books [159,106]. 16 In [178] the conditions were completely clarified by Zannier and a sharp bound on the number of solutions was given.…”

mentioning

confidence: 99%

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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mentioning

confidence: 99%

30 years of collaboration

Fuchs

Hajdu

2016

Period Math Hung

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“…, p + q}. As in the proof of [15,Corollary 2] it is easy to see by [15,Corollary 1(b)] that there are at most max{ord G n , ord H n } + p+q 2 solutions in every class containing distinct integers i, j in [1, p] …”

Section: Proof Of Theoremmentioning

confidence: 66%

“…The proof of this result follows the line of proof from [15,Corollary 2] and uses a result due to Shorey and Tijdeman (see [13, pp. 84-85] and [4,Lemma 3]).…”

Section: Resultsmentioning

confidence: 99%

“…The following proposition is a generalization of [15,Corollary 2] to the case of arbitrary (also non-simple) linear recurring sequences G n and H n given by…”

Section: Resultsmentioning

confidence: 99%

“…This equation can be understood as an identity in K[X, Y ]/(Q(X, Y )), which denotes the residue class ring of the curve Q(x, y) = 0. Using the ideas introduced in [15], we want to give necessary conditions under which the more general problem has at most finitely many solutions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Diophantine Equation G n (x) = G m (y) with Q (x, y)=0

Fuchs

Pethö

Tichy³

Diophantine Approximation

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Decomposable polynomials in second order linear recurrence sequences

2018

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Let (Gn(x)) ∞ n=0 be a d-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let m ≥ 2 be a given integer. We ask for n ∈ N such that the equation Gn(x) = g • h is satisfied for a polynomial g ∈ C[x] with deg g = m and some polynomial h ∈ C[x] with deg h > 1. We prove that for all but finitely many n these decompositions can be described in "finite terms" coming from a generic decomposition parameterized by an algebraic variety. All data in this description will be shown to be effectively computable.

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On the integer solutions of exponential equations in function fields

Cited by 16 publications

References 1 publication

30 years of collaboration

30 years of collaboration

On the Diophantine Equation G n (x) = G m (y) with Q (x, y)=0

Decomposable polynomials in second order linear recurrence sequences

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