Number Theory

    

Is there an Infinite Number in Which the Sum of the Divisors is the Square Number?

Authors: Minhyeok An

The numbers whose sum of divisors is a perfect square may initially appear to follow no specific pattern. However, through this research, I have identified a particular rule related to prime numbers. Furthermore, I establish that the existence of infinitely many numbers whose sum of divisors is a perfect square is a necessary and sufficient condition for the existence of an irreducible polynomial with integer coefficients that generates infinitely many prime numbers. Additionally, I explore its connection to Bunyakovsky's conjecture.

Comments: 16 Pages. If this paper contains no errors, resolving Bunyakovsky’s conjecture through this approac.h would hold even greater mathematical significance than previously recognized.

Download: PDF

Submission history

[v1] 2025-02-17 21:16:59
[v2] 2025-02-22 05:23:55

Unique-IP document downloads: 363 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus