Tag: integer factorization
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My Integer Factorization Study: A Slightly Cleaned-Up Result
Advertisements Let m=pq, where p and q are unknown odd prime numbers, be an integer we wish to factor. Let c=ceil(sqrt(m)) be the integer ceiling of the square root of m. Evaluate r1=c2-m. Evaluate r2=(c+1)2-m. If either r1 or r2 are perfect squares, this leads to a quick factorization due to c2-n2 being equal to…
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My Integer Factorization Study: An Important Quadratic Polynomial
Advertisements Well, I’m right back in the mess! Today’s epiphany of an interesting avenue to take took place, not in early hours of wakefulness, but as I was on my way to Wendy’s (the fast food place, not my wife’s place, which is currently a cabin by the beach – I’m envious). Let m be…
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My Integer Factorization Study: A Brief Anecdotal/Insight Update
Advertisements Along with my direct mathematical study of data and ways to gain insight into what is going on with Ceiling Squares, their remainders and ascents, and so on, I have been reading the free e-book I got with my AMS Membership: The Joy of Factoring by Samuel S. Wagstaff, Jr. It basically amounts to…
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Preparation and Apprehension
Advertisements My wife and I are spending some time with our out-of-state grandchildren, and with our daughter and son-in-law, in the State where I lived over half my life pursuing my Federal career. Also, I am using this opportunity to take delivery of a computer upgrade: replacing Christopher, my MacBook Pro I purchased last year…
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The Star
Advertisements Far, far more distant than Venus, its light not reaching us for uncountable years… Crowley’s card brings it close, almost immanent, associates it with that planet so close to us… He did not understand intergalactic distances as we do, but still, he might have understood something of the speed of light, the immensity of…
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My Integer Factorization Study: It’s Yrev, Very Good to See You Again, Old Friend.
Advertisements I decided to look at differences of squares near the values of numbers I wished to factor tonight. I took a particular randomly-generated semiprime m, and started generating differences of squares, sequentially, that would come out near m. The first graph I observed showed a triangle of fairly randomly distributed dots. But then I…
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My Integer Factorization Study: “Barbara, … we’re home.”
Advertisements After some study, the author has discovered that the ascent – the difference between the ceiling root of m and the value of s so that one can form a non-trivial s2-t2 expression of m – corresponds to the value of n one finds when expressing prime factors p and q in terms of…
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Laura P. On Studying Ascents
Advertisements I feel like I’m going to dream tonight. Big, bad ones. You know, the kind you like? [excerpt from Twin Peaks season 1 episode 7]
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The Ascent of m: A Concept Whose Properties I Shall Explore Soon
Advertisements The minuend of any such square-difference expression of m will then be greater than m’s ceiling square. Define the ascent of such a factorization or corresponding square-difference expression as the difference between the square root of the minuend in that expression and the ceiling root of m. EXAMPLES: The ascent of the trivial factorization…
