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 .
Stronger formedit
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:
(i) are pairwise coprime
(ii)
(iii) no proper subsum of equals
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 .
Referencesedit
Browkin, Jerzy; Brzeziński, Juliusz (1994). "Some remarks on the abc-conjecture". Math. Comp. 62 (206): 931–939. Bibcode:1994MaCom..62..931B. doi:10.2307/2153551. JSTOR 2153551.
Vojta, Paul (1998). "A more general abc conjecture". arXiv:math/9806171. Bibcode:1998math......6171V. {{cite journal}}: Cite journal requires |journal= (help)