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Matrices Reloaded

A return journey into Maths. Friday, 3 July 2015. RSA Factoring Challenge (part 6). I want to consider an example to show how we can attempt to find a solution to the eight simultaneous equations (1) to (8). I will start with an example where we know the two four digit primes p and q and then attempt to recover p and q from their product n using equations (1) to (8). Let p be 2029 and q be 4919 then their product n is 9980651. If we didn't know what p and q were then following our analysis in part (1).

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A return journey into Maths. Friday, 3 July 2015. RSA Factoring Challenge (part 6). I want to consider an example to show how we can attempt to find a solution to the eight simultaneous equations (1) to (8). I will start with an example where we know the two four digit primes p and q and then attempt to recover p and q from their product n using equations (1) to (8). Let p be 2029 and q be 4919 then their product n is 9980651. If we didn't know what p and q were then following our analysis in part (1).

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1 matrices reloaded

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matrices reloaded,then x,posted by,duncan hale sutton,no comments,email this,blogthis,share to twitter,share to facebook,share to pinterest,and b,coefficient a,and coefficient b,where i,then c i,and y,such that,and c,and x,end{pmatrix}$,via equation 8

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Matrices Reloaded | matrices-reloaded.blogspot.com Reviews

https://matrices-reloaded.blogspot.com

A return journey into Maths. Friday, 3 July 2015. RSA Factoring Challenge (part 6). I want to consider an example to show how we can attempt to find a solution to the eight simultaneous equations (1) to (8). I will start with an example where we know the two four digit primes p and q and then attempt to recover p and q from their product n using equations (1) to (8). Let p be 2029 and q be 4919 then their product n is 9980651. If we didn't know what p and q were then following our analysis in part (1).

INTERNAL PAGES

matrices-reloaded.blogspot.com

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Matrices Reloaded: December 2013

http://www.matrices-reloaded.blogspot.com/2013_12_01_archive.html

A return journey into Maths. Thursday, 19 December 2013. Just a quick progress report. I am still just about keeping up with the work but I can see that next week I will probably get behind because of the Christmas holidays. Never mind. In the mean time I have begun the geometry book GE3 on two-dimensional lattices. It's a bit of light relief to think about parallelograms and vectors. Monday, 9 December 2013. A periodic tiling is just a tiling that has a translation subgroup that is generated by two inde...

2

Matrices Reloaded: October 2014

http://www.matrices-reloaded.blogspot.com/2014_10_01_archive.html

A return journey into Maths. Monday, 20 October 2014. Gaussian Integers and Fermat's two square theorem. What is a Gaussian integer? These are a generalization of the ordinary set of integers Z and can be defined as the set of complex numbers. Mathbb{Z} left[i right]= left {a bi:a,b in mathbb{Z} right }$. Is it possible to find similarities between this set and the set of ordinary integers and if so what do these common properties tell us about the nature of integers in general? Z {1}z {2} = z {1} z {2} $.

3

Matrices Reloaded: January 2015

http://www.matrices-reloaded.blogspot.com/2015_01_01_archive.html

A return journey into Maths. Friday, 23 January 2015. The division property in integer-like sets. In ' Elements of Number Theory. I will attempt to go through both cases and explain how I see it. Firstly, the Gaussian integers. Suppose μ and β are the Gaussian integers. Where m, n, r and s are elements of Z and i=√-1. Then. Mu beta=m beta n beta i.(3)$. Now we have that. Beta i=ri si {2}=-s ri.(4)$. R,s) cdot(-s,r)=r(-s) sr=0.(5)$. Now what about the quadratic integers Z[√-2]? Mu=a b sqrt{-2}.(6)$. If we...

4

Matrices Reloaded: RSA Factoring Challenge (part 1)

http://www.matrices-reloaded.blogspot.com/2015/03/rsa-factoring-challenge-part-1.html

A return journey into Maths. Wednesday, 25 March 2015. RSA Factoring Challenge (part 1). In a diversion away from my continuing study of number theory, I have been thinking about the difficulty of factoring large integers. My attention was caught by the RSA Factoring Challenge. Which was set up by the RSA Laboratories to "learn about the actual difficulty of factoring large numbers of the type used in RSA keys." I have described RSA encryption. Wikipedia has a list of the RSA numbers. My first thought wa...

5

Matrices Reloaded: RSA Factoring Challenge (part 4)

http://www.matrices-reloaded.blogspot.com/2015/04/rsa-factoring-challenge-part-4.html

A return journey into Maths. Thursday, 16 April 2015. RSA Factoring Challenge (part 4). Looking back at my previous post. Is it possible to solve these eight simultaneous equations given that a number n is the product of two prime numbers p and q each of four digits long? The first thing to notice is that equation (1) is equivalent to. X {0}Y {0} equiv Z {0} ; mbox{(mod 10)}.(9)$. Which is as I discussed in part 1. So for a given Z. There are either two or three solutions for the pair (X. Is (3,7) (so Z.

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oumaths.wordpress.com

M381 exam | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2014/06/13/m381-exam

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Have to say, the exam yesterday seemed very fair and quite representative of past papers. Ran out of time (as with every exam I have ever done), so hoping I have enough marks in the bag. Did six questions from number theory and two and a bit from mathematical logic when the “pens down” comment came. That completes degree one (Open). Good luck to all for results day. June 13, 2014 at 5:41 PM.

oumaths.wordpress.com

M381 continued | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2014/02/02/m381-continued

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Or, should I say, continues. I have pretty much finished the logic books for the next assignment – TMA questions over the next couple of days. Then, it’s time for the number theory books – some good stuff in them, from the looks of it. So much so, that a poem I wrote aged 12 came back to me today – word for word – decades later. I’ve written it down.🙂. Placebo, maybe, but it’s working.

oumaths.wordpress.com

September | 2013 | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2013/09

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Archive for September, 2013. Next course and stuff. It’s been yonks since I’ve updated. Binned SM358 – no time – and managed a pass two on M337 complex analysis in the end – simply ran out of time in the exam, which I thought was pretty easy, to be fair, apart from me writing ever more slowly as the years go by. In other news, I have gone a bit programming mad. C# planned after Java.😉.

oumaths.wordpress.com

November | 2013 | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2013/11

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Archive for November, 2013. A cracking little watch. I thought this video was a cracker and ended up with several sheets of A4 of ideas to explore. Maybe others studying M381 will find it worthwhile, too. November 21, 2013 Categories: Uncategorized. Still messing around…. 8230; with the last two questions of the logic assignment questions. Wired on coffee right now. Constructing Unlimited R...

oumaths.wordpress.com

Result | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2014/07/27/result-2

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Just missed the necessary mark for a grade one on M381. So, grade two instead. Have claimed the Open degree. Have also enrolled on MT365 for next academic year – I have an old copy of the books here and have pretty much read them through on a first pass. MSXR209 residential course this week – assignment one done to bring with me. So, the next 12 months are:. It was filed under Uncategorized.

oumaths.wordpress.com

Open University bent my brain - Number Theory and Mathematical Logic for 2014 | maths study via The Open University | Page 2

https://oumaths.wordpress.com/page/2

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. M381 – some more done. NT3 and NT4 seemed reasonable to read. The NT assignment questions seemed quite removed from the material. But they got chipped away little by little and, I confess, I have had to spend more time on them than I think I should have. But I have solutions which appear to work, to the detriment of my sleeping pattern. ML2 and 3 – just lol. To that end, Q1-8 of TMA2 are do...

oumaths.wordpress.com

oumaths | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/author/oumaths

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Just missed the necessary mark for a grade one on M381. So, grade two instead. Have claimed the Open degree. Have also enrolled on MT365 for next academic year – I have an old copy of the books here and have pretty much read them through on a first pass. MSXR209 residential course this week – assignment one done to bring with me. So, the next 12 months are:. Did six questions from number th...

oumaths.wordpress.com

Continued fractions | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2014/03/10/continued-fractions

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. I thought this was a decent watch as a basic introduction to M381’s continued fractions. This entry was posted on March 10, 2014 by oumaths. It was filed under Uncategorized. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out.

oumaths.wordpress.com

June | 2014 | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2014/06

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Archive for June, 2014. Have to say, the exam yesterday seemed very fair and quite representative of past papers. Ran out of time (as with every exam I have ever done), so hoping I have enough marks in the bag. Did six questions from number theory and two and a bit from mathematical logic when the “pens down” comment came. That completes degree one (Open). Good luck to all for results day.

oumaths.wordpress.com

January | 2014 | Open University bent my brain - Number Theory and Mathematical Logic for 2014

https://oumaths.wordpress.com/2014/01

Open University bent my brain – Number Theory and Mathematical Logic for 2014. Maths study via The Open University. Archive for January, 2014. Well, away tomorrow after work, anyway. Q9 now done, I think with a thorough explanation of what’s going on, and some good insight bought into the bargain. Just need to photocopy it all in case it disappears in the post. I have had a quick skim read of ML 4-7, leaving 8 aside for now. It looks great – just what I hoped for. M381 – some more done. Re-read number 2 ...

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Matrices Reloaded

A return journey into Maths. Friday, 3 July 2015. RSA Factoring Challenge (part 6). I want to consider an example to show how we can attempt to find a solution to the eight simultaneous equations (1) to (8). I will start with an example where we know the two four digit primes p and q and then attempt to recover p and q from their product n using equations (1) to (8). Let p be 2029 and q be 4919 then their product n is 9980651. If we didn't know what p and q were then following our analysis in part (1).

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