A consequence of an effective form of the abc-conjecture

• Autorzy: Jerzy Browkin
• Języki publikacji: EN

Abstrakty

EN

T. Cochrane and R. E. Dressler [CD] proved that the abc-conjecture implies that, for every 𝜀 > 0, the gap between two consecutive numbers A<C having the same prime factors is ≫ $A^{1/2-𝜀}$. In the present paper, from a weak effective form of the abc-conjecture we deduce that A-C > $A^{0.4}$ with two exceptions given in Table 2.

Słowa kluczowe

EN

abc-extremal examples; gaps; abc-conjecture

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 82
• Numer: 1
• Strony: 79-84

Daty

wydano

1999

otrzymano

1999-05-04

Twórcy

autor

Jerzy Browkin

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [B] J. Browkin, The abc-conjecture, to appear.
• [CD] T. Cochrane and R. E. Dressler, Gaps between integers with the same prime factors, Math. Comp. 68 (1999), 395-401.