Tag: mathematics

• My Integer Factorization Study: May 7 2022 4:29pm Eastern Update

Advertisements This morning’s Tiny Eureka demonstrates itself right now to be a trivial finding, and therefore unlikely to lead me to a Big Eureka.

• My Integer Factorization Study: Tiny Eureka! (or Should I Say “Woof!”?)

Advertisements I am finally barking up the correct tree, so to speak, and I have found the little squirrel I sought. From the beginning, with gusto! (By the way, the relationship I am about to describe took a while to hammer out on paper, and a great deal longer to get right in Perl code.) […]

• My Integer Factorization Study: Discouraged, but Then Renewed in Hope

Advertisements UPDATE: the sometimes triangular tables of values I have been building over the last several days have borne fruit, so to speak. I do not know where this will lead me, or how much easier it will make the task of integer factorization, but I have found a relationship between the product m of […]

• My Integer Factorization Study: Closer, but No Cigar (Squirrel?) Yet

Advertisements Last night and this morning, I began looking at the behavior of the remainder r = s2 – m, where m is the product of distinct primes p and q, p < q, and s is the smallest integer greater than the square root of m. I began to build a kind of triangular […]

• My Integer Factorization Study: Boiling It Down

Advertisements It now seems that the task at hand is this: Given two linear equations with integer coefficients: y1 = a1x + b1, and y2 = a2x + b2, find the integer values of x, if any, where y1 is an integer multiple of y2. y1 = n*y2 when x = (b2n – b1)/(a1 – […]

• My Mathematical/Number Study: What Got Me Up Early This Morning

Advertisements Consider the positive integer m which is the product of distinct primes p and q. Consider s, the smallest integer greater than the square root of m, and the difference r = s^2 – m. p will be less than s, and q will be greater than s. Thus p = s – c1 […]