Tag: number theory

Ceiling Squares: My New Mathematical Study
Advertisements Welcome to my new mathematical study! My work on integer factorization led, not to any new discoveries in number theory, but to a way of organizing the odd positive integers that lends itself to visualization and can provide insight: the Ceiling Square. Simply put – or, at least, as compactly phrased as I can […]

[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 […]

My Integer Factorization Study: A Mathematical Report
Advertisements I have begun writing a mathematical report, in my Google Docs shareable files, summarizing the basic principles I am examining and the work I have done, with discoveries I have made, so far. The report is here. (clickable link)