Tag: integer factorization

Ceiling Squares: You Can Generalize, if You Wanna, but You Will Lose the Squareness
Advertisements I thought of, and actually fiddled with, a generalization of ceiling squares to include all positive integers, excluding perfect squares, both even and odd. Though not a genuine problem with this, there are some tradeoffs that make me say “Why bother?” For a given perfect square ceiling s2, there will now be 2s2 rows […]

The Latest Math Idea to Get Me Up Early
Advertisements All possible factorizations into two factors of the positive integers correspond to all integer points on the family of curves y=m/x, for m an element of the infinite set {1,2,3,4,5,…}, and we can restrict our attention, thanks to mirror symmetry, to the points where x and y are greater than zero (symmetric by Cartesian […]

Ceiling Squares: Final Paper Is Up, on Google Docs
Advertisements Below is a link to the more or less official description of a very, very intense, enlightening, and enjoyable mathematical study I have just completed, and it includes software for those who might wish to run Perl routines to illustrate some of the ideas I explored. https://docs.google.com/document/d/1or9NQfCKM11MhOoZ_nXe0G8uuVLIyeUpPalve9yuveg/edit?usp=sharing

[Archived Post] My Integer Factorization Study: Current Idea Showing Potential
Advertisements EDIT: This was an article I wrote a while ago, that still now seems to be in DRAFT status. I will “publish” it now so that it is on the study record. Right now, what attracts my attention is the fact I figured out on paper that n = (c12r)/(sc1). This implies that sc1 […]

My Integer Factorization Study: Final Report (Google Docs)
Advertisements Here is the link to my Google Docs summary of the mathematical study I have just completed, including all the information in my previous blog post, and more. https://docs.google.com/document/d/1OP7B7STeHaVhFaRU_DfjVCx2QUspB4jvPFUAlyhh8GI/edit?usp=sharing

My Integer Factorization Study: Maybe No New Discoveries, but a Fairly Good Program (I Think)
Advertisements After extensive study, and a great many discoveries which seemed exciting to me but that after investigation boiled down to properties of established concepts, I have been able to construct an algorithm that uses the difference between m and the smallest greater perfect square s to search for appropriate values of c and thus […]

My Integer Factorization Study – Breakthrough! (If Not Precisely Eureka!)
Advertisements I believe now that I can completely characterize a relationship between the quantities m (number to be factored), s (least perfect square > m), r (the difference between s2 and m) and a reduced set of candidate values for c1, which will also give c2, n, p, and q. The details are in my […]

My Integer Factorization Study: Woof?
Advertisements The latest revelations, which came almost unbidden despite my expressed desire to take a break from this study, turned out to be exciting ones, and I am trying to remain calm. I have found relationships between the value of r (which is the difference between the square of s (the integer ceiling of the […]

My Integer Factorization Study: An Extended Pause
Advertisements I am pausing in my study of these numbers and their behaviors for a while, for two good reasons: The seeming chaos of some of the relationships between numbers was just too much for my brain to handle. I need to concentrate on the extensive cleaning tasks I need to complete in order to […]