NishMath - #Insights

Terence Tao has recently uploaded a paper to the arXiv titled "Decomposing a factorial into large factors." The paper explores a mathematical quantity, denoted as t(N), which represents the largest value such that N! can be factorized into t(N) factors, with each factor being at least N. This concept, initially introduced by Erdös, delves into how equitably a factorial can be split into its constituent factors.

Erdös initially conjectured that an upper bound on t(N) was asymptotically sharp, implying that factorials could be split into factors of nearly uniform size for large N. However, a purported proof by Erdös, Selfridge, and Straus was lost, leading to the assertion becoming a conjecture. The paper establishes bounds on t(N), recovering a previously lost result. Further conjectures were made by Guy and Selfridge, exploring whether relationships held true for all values of N.

On March 30th, mathematical enthusiasts celebrated facts related to the number 89. Eighty-nine is a Fibonacci prime, and patterns emerge when finding it's reciprocal. Also, the number 89 can be obtained by a summation of the first 5 integers to the power of the first 5 Fibonacci numbers. 89 is also related to Armstrong numbers, which are numbers that are the sum of their digits raised to the number of digits in the number.


References :

• beuke.org: Your browser does not support the audio element. Profunctor optics are a modern, category-theoretic generalization of optics – bidirectional data accessors used to focus on and update parts of a data structure.
• What's new: I;ve just uploaded to the arXiv the paper “Decomposing a factorial into large factors“. This paper studies the quantity , defined as the largest quantity such that it is possible to factorize into factors , each of which is at least .

Classification:

• HashTags: #Mathematics #Research #FunFacts
• Target: Knowledge
• Product: General
• Feature: Insights
• Type: Research
• Severity: Informative