# Squarefree integers and the $abc$ conjecture

@inproceedings{Batang2021SquarefreeIA, title={Squarefree integers and the \$abc\$ conjecture}, author={Zenon B. Batang}, year={2021} }

For coprime positive integers a, b, c, where a+ b = c, gcd(a, b, c) = 1 and 1 ≤ a < b, the famous abc conjecture (Masser and Oesterlè, 1985) states that for ε > 0, only finitely many abc triples satisfy c > R(abc), where R(n) denotes the radical of n. We examine the patterns in squarefree factors of binary additive partitions of positive integers to elucidate the claim of the conjecture. With abc hit referring to any (a, b, c) triple satisfying R(abc) < c, we show an algorithm to generate hits… Expand

#### References

SHOWING 1-10 OF 20 REFERENCES

Some remarks on the abc -conjecture

- Mathematics
- 1994

Let r(x) be the product of all distinct primes dividing a nonzero integer x . The abc-conjecture says that if a, b, c are nonzero relatively prime integers such that a + b + c = 0, then the biggest… Expand

The ABC's of Number Theory

- Mathematics
- 2007

The ABC conjecture is a central open problem in modern number theory, connecting results, techniques and questions ranging from elementary number theory and algebra to the arithmetic of elliptic… Expand

Lecture on the abc Conjecture and Some of Its Consequences

- Mathematics
- 2015

The abc conjecture was proposed in the 1980s by J. Oesterle and D.W. Masser. This simple statement implies a number of results and conjectures in number theory. We state this conjecture and list a… Expand

The abc Conjecture

- Mathematics
- 1999

Let’s start with a theorem about polynomials. You probably think that one knows everything about polynomials. Most mathematicians would think that, including myself. It came as a surprise when R. C.… Expand

Graphs on Surfaces and Their Applications

- Mathematics
- 2003

0 Introduction: What is This Book About.- 1 Constellations, Coverings, and Maps.- 2 Dessins d'Enfants.- 3 Introduction to the Matrix Integrals Method.- 4 Geometry of Moduli Spaces of Complex Curves.-… Expand

Nouvelles approches du «théorème» de Fermat

- Mathematics
- 1988

© Société mathématique de France, 1988, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les… Expand

Questions about Powers of Numbers

- Mathematics
- 2000

A drift compensation circuit for a cascade encoder used in a pulse code modulation communication system, including at least first, second through m-th encoders connected in cascade for converting an… Expand

Note on a conjecture of Szpiro. Séminaire sur les pinceaux de courbes elliptiques, Paris, France

- 1988