The number of abc-equations cⁿ=a+b stisfying the strong abc-conjecture

2011/09/22 by Constantine M. Petridi, Petridi, Constantine M.
Computer Science · Mathematics · #11-xx #Advanced Mathematical Physics Problems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11-xx

paper · pdf · doi:10.48550/arxiv.1109.4762

3 pages

arxiv created 2011/09/22 · openalex publication_date 2011/09/22 · arxiv updated 2011/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the frequency of abc equations cⁿ = a+b satisfying the strong abc - conjecture is phi(cⁿ)/2+o(phi(cⁿ)/2), for n going to infinity.

Citations

• A strong "abc-conjecture" for certain partitions a+b of c

Related

• The number of equations c=a+b satisfying the abc-conjecture
• Applications of the abc conjecture to powerful numbers
• Finiteness properties of abc-equations c = a+b
• Probable Counterexamples of the ABC Conjecture
• A more general abc conjecture