International Journal of Innovative Research in Engineering and Management
Year: 2025, Volume: 13, Issue: 2
First page : ( 54) Last page : ( 57)
Online ISSN : 2350-0557.
DOI: 10.55524/ijircst.2025.13.2.8 |
DOI URL: https://doi.org/10.55524/ijircst.2025.13.2.8
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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0)
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Saroj Kumar Patra , Subhasmita Pattnaik
The ABC Conjecture is one of the most beautiful conjectures in number theory; it reveals a very strong link between the additive and multiplicative characteristics of integers. The conjecture holds (with few exceptions) that if three positive numbers a,b and c are a coprime and a+b=c, then the c is not significantly larger than the Multiplication of distinctive prime factors of abc (written rad (abc)). It presents an integrated review of the concept, some theoretical consequences, important examples of the concept; and potential uses in computational number theory, cryptography, and elsewhere.
[1] J. Oesterlé and D. Masser, “The ABC Conjecture in Number Theory,” Various Academic Surveys, 1985.
[2] S. Mochizuki, “Inter-Universal Teichmüller Theory: A Proposed Proof of the ABC Conjecture,” 2012. Available from: https://shorturl.at/Zk5AF
[3] Wikipedia contributors, “ABC Conjecture,” Wikipedia, The Free Encyclopedia. Available from: https://en.wikipedia.org/wiki/ABC_conjecture
[4] A. Granville, “ABC allows us to count squarefrees,” Int. Math. Res. Not., vol. 1998, no. 19, pp. 991–1009, 1998. Available from: https://dms.umontreal.ca/~andrew/PDF/polysq3.pdf
[5] N. D. Elkies, “ABC implies Mordell,” Int. Math. Res. Not., vol. 1991, no. 7, pp. 99–109, 1991. Available from: https://pazuki.perso.math.cnrs.fr/index_fichiers/Elkies91.pdf
[6] Additional computational studies and reviews on the impact of the ABC Conjecture in applied number theory can be found in specialized journals.
Faculty, Mathematics, IPSAR, chauliaganj,cuttack, India
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