![]() | This article may be too technical for most readers to understand.(July 2015) |
![]() | This article includes a
list of references,
related reading, or
external links, but its sources remain unclear because it lacks
inline citations. (November 2020) |
In number theory the n conjecture is a conjecture stated by Browkin & Brzeziński (1994) as a generalization of the abc conjecture to more than three integers.
Given , let satisfy three conditions:
First formulation
The n conjecture states that for every , there is a constant , depending on and , such that:
where denotes the radical of the integer , defined as the product of the distinct prime factors of .
Second formulation
Define the quality of as
The n conjecture states that .
Vojta (1998) proposed a stronger variant of the n conjecture, where setwise coprimeness of is replaced by pairwise coprimeness of .
There are two different formulations of this strong n conjecture.
Given , let satisfy three conditions:
First formulation
The strong n conjecture states that for every , there is a constant , depending on and , such that:
Second formulation
Define the quality of as
The strong n conjecture states that .
{{
cite journal}}
: CS1 maint: unflagged free DOI (
link)![]() | This article may be too technical for most readers to understand.(July 2015) |
![]() | This article includes a
list of references,
related reading, or
external links, but its sources remain unclear because it lacks
inline citations. (November 2020) |
In number theory the n conjecture is a conjecture stated by Browkin & Brzeziński (1994) as a generalization of the abc conjecture to more than three integers.
Given , let satisfy three conditions:
First formulation
The n conjecture states that for every , there is a constant , depending on and , such that:
where denotes the radical of the integer , defined as the product of the distinct prime factors of .
Second formulation
Define the quality of as
The n conjecture states that .
Vojta (1998) proposed a stronger variant of the n conjecture, where setwise coprimeness of is replaced by pairwise coprimeness of .
There are two different formulations of this strong n conjecture.
Given , let satisfy three conditions:
First formulation
The strong n conjecture states that for every , there is a constant , depending on and , such that:
Second formulation
Define the quality of as
The strong n conjecture states that .
{{
cite journal}}
: CS1 maint: unflagged free DOI (
link)