Finiteness properties of abc-equations c = a+b

2012/12/18 by Constantin M. Petridi, Petridi, Constantin M.
Computer Science · Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.1212.4280

4 pages

arxiv created 2012/12/18 · openalex publication_date 2012/12/18 · arxiv updated 2012/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify integer abc-equations c = a + b (to be defined), according to their radical R(abc) and prove that the resulting equivalence classes contain only a finite number of such equations. The proof depends on a 1933 theorem of Kurt Mahler.

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