On Baker’s explicit abc-conjecture

Kwok Chi Chim, Tarlok Nath Shorey, Sneh Bala Sinha

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

We derived from Baker’s explicit abc-conjecture that a + b = c, where a, b and c are relatively prime positive integers, implies that c < N1.72 for N ≥ 1 and c < 32N1.6 for N ≥ 1. This sharpens an estimate of Laishram and Shorey. We also show that it implies c < 5 6N1+G(N) for N ≥ 3, and c < 6 5N1+G1(N) for N ≥ 297856, where G(N) and G1(N) are explicitly given positive valued decreasing functions of N tending to zero as N tends to infinity. Finally, we give applications of our estimates on triples of consecutive powerful integers and generalized Fermat equation.

Originalspracheenglisch
Seiten (von - bis)435-453
Seitenumfang19
FachzeitschriftPublicationes Mathematicae
Jahrgang94
Ausgabenummer3-4
DOIs
PublikationsstatusVeröffentlicht - 1 Jan 2019

ASJC Scopus subject areas

  • !!Mathematics(all)

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