A consequence of an effective form of the abc-conjecture

Jerzy Browkin

Displaying similar documents to “A consequence of an effective form of the abc-conjecture”

Corrigendum to the paper "On the 2-primary part of a conjecture of Birch and Tate" (Acta Arith. 43 (1983), 69-81)

Jerzy Urbanowicz (1993)

Acta Arithmetica

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On smooth integers in short intervals under the Riemann Hypothesis

Ti Zuo Xuan (1999)

Acta Arithmetica

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On A Combinatorial Problem Connected withFactorizations

Weidong Gao (1997)

Colloquium Mathematicae

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On prime factors of integers of the form (ab+1)(bc+1)(ca+1)

K. Győry, A. Sárközy (1997)

Acta Arithmetica

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1. Introduction. For any integer n > 1 let P(n) denote the greatest prime factor of n. Győry, Sárközy and Stewart [5] conjectured that if a, b and c are pairwise distinct positive integers then (1) P((ab+1)(bc+1)(ca+1)) tends to infinity as max(a,b,c) → ∞. In this paper we confirm this conjecture in the special case when at least one of the numbers a, b, c, a/b, b/c, c/a has bounded prime factors. We prove our result in a quantitative form by showing that if is a finite set of triples...

On transience conditions for Markov chains.

Foss, S. G., Denisov, D. Eh. (2001)

Sibirskij Matematicheskij Zhurnal

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Inequalities concerning the function π(x): Applications

Laurenţiu Panaitopol (2000)

Acta Arithmetica

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Introduction. In this note we use the following standard notations: π(x) is the number of primes not exceeding x, while $θ (x) = \sum_{p \leq x} l o g p$ . The best known inequalities involving the function π(x) are the ones obtained in [6] by B. Rosser and L. Schoenfeld: (1) x/(log x - 1/2) < π(x) for x ≥ 67 (2) x/(log x - 3/2) > π(x) for $x > e^{3 / 2}$ . The proof of the above inequalities is not elementary and is based on the first 25 000 zeros of the Riemann function ξ(s) obtained by D. H. Lehmer [4]. Then Rosser, Yohe...

Discrete excursions.

Bousquet-Mélou, Mireille (2006)

Séminaire Lotharingien de Combinatoire [electronic only]

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Effective solution of families of Thue equations containing several parameters

Clemens Heuberger, Robert F. Tichy (1999)

Acta Arithmetica

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On the frequencies of large values of divisor functions

Karl K. Norton (1994)

Acta Arithmetica

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A note on the equation $a x^{n} - b y^{n} = c$

Maurice Mignotte (1996)

Acta Arithmetica

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