On the Radical of Multiperfect Numbers and Applications
Number Theory
2019-01-01 v1
Abstract
It is conjectured that for a perfect number We prove bounds on the radical of multiperfect number depending on its abundancy index. Assuming the ABC conjecture, we apply this result to study gaps between multiperfect numbers, multiperfect numbers represented by polynomials. Finally, we prove that there are only finitely many multiperfect multirepdigit numbers in any base where the number of digits in the repdigit is a power of This generalizes previous works of several authors including O. Klurman, F. Luca, P. Polack, C. Pomerance and others.
Keywords
Cite
@article{arxiv.1812.11239,
title = {On the Radical of Multiperfect Numbers and Applications},
author = {Nithin Kavi and Xinyi Zhang and Viraj Jayam and Ajit Kadaveru},
journal= {arXiv preprint arXiv:1812.11239},
year = {2019}
}