Tag: factorization

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 […]

My Number Study: Possible Breakthrough?
Advertisements This is a continuation of progress reports on a number study of the integer factorization problem I have been conducting this Spring. Last night, in working through my calculations to see which quantities involved I could express in terms of other quantities, I came upon one that surprised me, and I wonder if the […]

My Mathematical Study: A Brief Revelation/Realization
Advertisements When m is the product of two odd primes p and q, with p < q, and m is also equal to s^2 – r where s is the integer ceiling of the square root of m, the polynomial x^2 + n*x – (r + s*n) for the positive integer n that allows it […]

My Mathematical Study: The Current Integer Factorization Tree Up Which I’m Barking
Advertisements Let m = p * q denote the positive integer that is the product of prime numbers p and q. Determine s as the integer ceiling of the square root of m. If s is a perfect square, then p = q = s. Otherwise, perform the following steps: Determine r = s^2 – […]