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 2005-03-08, 14:14 #1 1260   Feb 2003 25 Posts Is this a feasible factoring method? Let N be a number that is proven to be composite but whose factors are unknown. Let F be a number less than the square root of N. Then N = b mod F. Increase F by 1, and b decreases by a certain amount. Further increase of F causes further decrease of b until b reaches a relative minimum and jumps back to a large value. If the relative minimum of b is zero, then we have a factor. But if this procedure is applied to large numbers, it would take quite a while before we arrive at a relative minimum of zero. My first question is: Is it possible to determine the relative minimum value for a particular F? I.e., If N = b mod F = c mod F+1, where N,F,b,c are known, can the relative minimum be identified from those values alone? My second question is: Is there a derivative for N = y mod x? If there is, can equating y' to zero identify ALL the minimum values?
2005-03-08, 14:26   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by 1260 Let N be a number that is proven to be composite but whose factors are unknown. Let F be a number less than the square root of N. Then N = b mod F. Increase F by 1, and b decreases by a certain amount. Further increase of F causes further decrease of b until b reaches a relative minimum and jumps back to a large value. If the relative minimum of b is zero, then we have a factor. But if this procedure is applied to large numbers, it would take quite a while before we arrive at a relative minimum of zero. My first question is: Is it possible to determine the relative minimum value for a particular F? I.e., If N = b mod F = c mod F+1, where N,F,b,c are known, can the relative minimum be identified from those values alone? My second question is: Is there a derivative for N = y mod x? If there is, can equating y' to zero identify ALL the minimum values?
May I suggest that before you discuss this subject further that you go learn
some mathematics? It is clear that you are ignorant of even the basics.

(1) Let N = (10^113-1)/9. Let F = 17

Then N mod F is 1. Increase F by 1. Explain how b decreases...
And your statement 'b decreases by a certain amount' is hand waving
nonsense. Beyond the simple fact that the statement is fault, the phrase
'by a certain amount' is so totally lacking in precision as to be meaningless.

Didn't you even bother to try some tiny examples before posting this nonsense???? It is gibberish. As is the talk about a 'relative minimum'

Your question about derivatives shows that you do not understand what a
derivative is. Why then are you even discussing them?

Before one begins a discussion of this type it is imperative that you do
You have done none of this. You are a troll. Go away.

 2005-03-08, 21:33 #3 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101×103 Posts 10,103 Posts Bob comes off a little strong, but he is correct in suggesting that you try your method out quite a bit, before you suggest that it may work. Studying up is good. (Bob is a true expert.) Here is a graph of an example of why your idea won't work. I took a number 1373 (prime) and used mod and graphed the results. Across the bottom is the divisor and up the side is the remainder. See how it is saw toothed? Even if the number had a factor, a similar pattern would be seen. mod values tend to swing around alot. Attached Thumbnails   Last fiddled with by Uncwilly on 2005-03-08 at 21:36
 2005-03-09, 07:40 #5 TTn   100101102 Posts ""
 2005-03-09, 09:14 #6 garo     Aug 2002 Termonfeckin, IE ACC16 Posts 1260, I hope Bob's response doesn't make you feel too unwelcome. While others on this forum may not have the same level of mathematical training, they are not as harsh or as judgemental
2005-03-09, 11:39   #7
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
(1) People who post in a PUBLIC FORUM have an obligation to do their homework before they start making PRONOUNCEMENTS.

rather bold pronouncements. It was `totally clear that he/she did not spend
even 30 seconds checking these pronouncements because a trivial check
would have revealed that they were wrong.

(3) One thing I do not have in abundance is time. When someone asks about
a 'method' it is their OBLIGATION to have at least done some preliminary
checking. To do otherwise is rude to others who read the post.

(4) When someone talks about a 'derivative' for a function defined only on the
integers it IS clear that this person does not have even the minimal background to try to discuss this material.

(5) I am hardly 'great' in math. But before I make some posting in a topic
about which I know little (let's say Galois Cohomology for example), I take
the time to read and study. To do otherwise shows discourtesy to the people
I would be asking for help.

PEOPLE HAVE AN OBLIGATION TO DO AT LEAST SOME PREPARATION BEFORE
WASTING THE TIME OF OTHERS.

If the people in this forum want help, it is imperative that they first
DO THEIR HOMEWORK. There is nothing more aggravating to a teacher than
someone who asks for help without having done their homework. It is too
bad that you don't understand this obligation.

2005-03-09, 14:36   #8
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

10,103 Posts

Quote:
 Originally Posted by R.D. Silverman (1) People who post in a PUBLIC FORUM have an obligation to do their homework before they start making PRONOUNCEMENTS.
I agree that folks should try to look into things, however this is more of a learning forum, rather than a forum exclusive to working math majors.
Quote:
 (3) One thing I do not have in abundance is time.
Quote:
 (4) When someone talks about a 'derivative' for a function defined only on the integers it IS clear that this person does not have even the minimal background to try to discuss this material.
At times people have an idea and not the technical vocabulary to express it. Many of the better teachers/lectures and those that help spread scientific knowledge to the public are able to express the concepts without relying upon the jargon.
Quote:
 (5) I am hardly 'great' in math. But before I make some posting in a topic about which I know little (let's say Galois Cohomology for example), I take the time to read and study. To do otherwise shows discourtesy to the people I would be asking for help.
Many of us are so ignorant (as opposed to stupid), that we have no clue what Galois Cohomology is. A resounding rebuke is best delivered by a friend and not a stranger.
Quote:
 PEOPLE HAVE AN OBLIGATION TO DO AT LEAST SOME PREPARATION BEFORE WASTING THE TIME OF OTHERS.
And people have an obligation to manners when posting in a public forum. Calling someone a troll for posting an on topic question is a bit caustic.
Quote:
 There is nothing more aggravating to a teacher than someone who asks for help without having done their homework. It is too bad that you don't understand this obligation.
While I understand this, I try to "bring them along" nonetheless. The best teachers deal with people where they are, not where they should be. Less than desireable behaviour by another does not excuse our own.

2005-03-09, 14:47   #9
1260

Feb 2003

25 Posts

Quote:
 Originally Posted by R.D. Silverman May I suggest that before you discuss this subject further that you go learn some mathematics? It is clear that you are ignorant of even the basics. To start with your first (erroneous) claim. (1) Let N = (10^113-1)/9. Let F = 17 Then N mod F is 1. Increase F by 1. Explain how b decreases...
Well, I guess I was not clear enough about the value of F. I was actually referring to a value at the top of one of the curves as illustrated by Uncwilly. If it were located there, b would decrease.

However, when b = 1, there is still a possibility of b decreasing if F+1 was a factor of N. However, if it was not a factor, it would shoot up to a relative maximum.

Last fiddled with by 1260 on 2005-03-09 at 14:54

2005-03-09, 14:53   #10
1260

Feb 2003

408 Posts

Quote:
 Originally Posted by Uncwilly Bob comes off a little strong, but he is correct in suggesting that you try your method out quite a bit, before you suggest that it may work. Studying up is good. (Bob is a true expert.) Here is a graph of an example of why your idea won't work. I took a number 1373 (prime) and used mod and graphed the results. Across the bottom is the divisor and up the side is the remainder. See how it is saw toothed? Even if the number had a factor, a similar pattern would be seen. mod values tend to swing around alot.

It's okay. I've received stronger words than those. I guess that's part of learning. Don't be afraid to be called a troll (especially if you're one ).

Yes, that's what I was after-- the lower ends of the swings. Isn't there a faster way to determine them without checking all values?

Last fiddled with by 1260 on 2005-03-09 at 14:58

2005-03-09, 15:03   #11
1260

Feb 2003

25 Posts

Quote:
 Originally Posted by R.D. Silverman ... (4) When someone talks about a 'derivative' for a function defined only on the integers it IS clear that this person does not have even the minimal background to try to discuss this material. ....
Can someone please explain to me why you can't get the derivative of a function that is defined only on the integers?

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