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Article
Peer-Review Record

Minimality Conditions Equivalent to the Finitude of Fermat and Mersenne Primes

by Menachem Shlossberg
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Submission received: 7 April 2023 / Revised: 21 May 2023 / Accepted: 26 May 2023 / Published: 31 May 2023
(This article belongs to the Special Issue Advances in Applied Algebra, Combinatorics and Computation)

Round 1

Reviewer 1 Report

 

Review report on “Minimality conditions equivalent to the finitude of Fermat and Mersenne primes”

 

This paper is concerned with the finitude of Fermat and Mersenne primes. The author characterizes these primes in terms of topological minimality of matrix groups, and shows that the finitude of Fermat and composite Fermat numbers is equivalent to certain conditions involving quadratic forms. The paper provides criteria for the minimality (and total minimality) of certain matrix groups, and extends some results from previous research.

 

The paper is well-organized and clearly written, with a concise abstract that summarizes the main findings.

 

Overall, this paper offers useful insights into the relationship between number theory and matrix groups, and sheds new light on the characterization of Fermat and Mersenne primes.

 

All in all, I recommend the paper to be accepted.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Outstanding work! My congratulations on this occasion. 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

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