The Extended Generating Function of the Radical of n and the abc-Conjecture

2018/02/08 by Constantin M. Petridi, Petridi, Constantin M.
Computer Science · Mathematics · #Advanced Mathematical Identities #Advanced Mathematical Theories #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1802.02770

openalex publication_date 2018/02/08 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28

Abstract

An extended generating series of the radical of n, involving two variables, leads to an identity in said variables, which proves Bombieri's abc-Conjecture for certain sets of integers.

Citations

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

Related

• The abc-conjecture is true for at least N(c), 1 ≤ N(c) <ϕ(c)/2, partitions a, b of c
• Probable Counterexamples of the ABC Conjecture
• A more general abc conjecture
• A strong "abc-conjecture" for certain partitions a+b of c
• Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases