Tag: number theory

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…

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…