Integer as sum of two squares of integers - Page 6

xilman · 2012-03-25, 19:14

Quote:

Originally Posted by R.D. Silverman

When have I been unwilling to teach?

However, I can't give an entire course in number theory in this venue.
Nor can I raise people's IQ.

I will however note that M919 had ALREADY been done by SNFS.
That's the first clue. The second is that M919 is not the sum of two
squares. Nor is any Mersenne number. This would be immediately
obvious to anyone who has done even the tiniest bit of study about
this subject. But for some reason, people keep wanting to post herein
while being totally clueless about the subject they are trying to discuss.

The final clue has nothing to do with number theory, per se. A
moment's thought by any right thinking person would reveal that if
Batalov had a new method powerful enough to factor M919
that he would be announcing it to the world!

"You can lead a horse's ass to knowledge, but you can't make him think."

Thank you! You rose to the bait and helped dispel some ignorance.

davieddy · 2012-03-25, 21:57

Quote:

Originally Posted by R.D. Silverman

Ignorance is a dangerous thing.

And is also bliss.
Now a little learning is a different ballpark.

science_man_88 · 2012-03-25, 22:45

Quote:

Originally Posted by R.D. Silverman

When have I been unwilling to teach?

However, I can't give an entire course in number theory in this venue.
Nor can I raise people's IQ.

I will however note that M919 had ALREADY been done by SNFS.
That's the first clue. The second is that M919 is not the sum of two
squares. Nor is any Mersenne number. This would be immediately
obvious to anyone who has done even the tiniest bit of study about
this subject. But for some reason, people keep wanting to post herein
while being totally clueless about the subject they are trying to discuss.

The final clue has nothing to do with number theory, per se. A
moment's thought by any right thinking person would reveal that if
Batalov had a new method powerful enough to factor M919
that he would be announcing it to the world!

"You can lead a horse's ass to knowledge, but you can't make him think."

http://www.khanacademy.org/exercisedashboard?move_on=1 this is a test you can put people to is it up to your standards ? it was pointed out in another thread.

CRGreathouse · 2012-03-26, 02:01

Quote:

Originally Posted by science_man_88

http://www.khanacademy.org/exercisedashboard?move_on=1 this is a test you can put people to is it up to your standards ? it was pointed out in another thread.

It doesn't really have any number theory in it. It looks like it covers precollege mathematics only.

science_man_88 · 2012-03-26, 12:02

Quote:

Originally Posted by CRGreathouse

It doesn't really have any number theory in it. It looks like it covers precollege mathematics only.

we'll it's already told me where my knowledge lacks most of them take me 5-10 questions to pass one took me 34 to pass.

sascha77 · 2012-03-26, 21:08

I think the reason why a mersenne number can not expressed as the sum of two squared numbers, is shown in this pdf (On Page 2. Proposition 1)
http://www.math.uga.edu/~pete/4400twosquares.pdf

This is a proof, that NONE number n with the form: $n \equiv 3 \;(\;mod \;4\;)$ can be expressed as sum of two squares.

But every mersenne number has this form.

$2^p \equiv 0 \;(\;mod \;4\;)$

-> $2^p-1 \equiv -1 \equiv 3 \;(\;mod\;4\;)$

CRGreathouse · 2012-03-26, 22:36

Quote:

Originally Posted by science_man_88

we'll it's already told me where my knowledge lacks most of them take me 5-10 questions to pass one took me 34 to pass.

I think it's fantastic that you're using that, since it shows you what you need. You then know what to ask for help on; good stuff!

science_man_88 · 2012-03-26, 22:41

Quote:

Originally Posted by CRGreathouse

I think it's fantastic that you're using that, since it shows you what you need. You then know what to ask for help on; good stuff!

yeah the sad part is the one I failed to get quickly ( admittedly I rush a little) was supposedly basic and terminology related.

CRGreathouse · 2012-03-26, 22:55

Quote:

Originally Posted by science_man_88

yeah the sad part is the one I failed to get quickly ( admittedly I rush a little) was supposedly basic and terminology related.

It's fantastic to learn that a mistake is due to a simple problem like misunderstanding terminology. Fix it up and move on. :)

science_man_88 · 2012-03-31, 22:24

Quote:

Originally Posted by Batalov

I found a brilliant and totally novel method of factoring large numbers.
I take any QNR of the cube of the sum of digits of the number to be factored and iterate by cubing this number and adding 13 modulo the number until I find a sum of squares.

Here's is my factorization of 2^919-1 =

Code:

33554520197234177 * 
152651074082705418105275481349108130060432918483467580289744030754735302146132556930363149457078636855455429731914714272974721 * 
865197224619933841837007366307939597646479749067444492477633169221316684482535898528285342696392522185018693261171052634586455801136511

This should end any discussion about validity of my algorithm written above.

13 modulo the number so 13 if n>13 ? if so that speeds it up for me.now just a sum of squares check needed and I can complete a brute force code at very least.

science_man_88 · 2012-03-31, 23:40

Quote:

Originally Posted by science_man_88

now just a sum of squares check needed and I can complete a brute force code at very least.

Code:

m=vector(100,n,if(n==1,2));for(x=2,100,m[x]=m[x-1]+(x\2)+((x\2)+1));m

this covers a lot of cases but not all of them. edit: DOH !!

Code:

m=[];for(x=1,100,for(y=1,100,m=concat(m,x^2+y^2)));m=vecsort(m,,8)

rest of the code:

Code:

(19:35)>?LQNR
LQNR(n)=a=vector(n-1,y,y);for(x=1,#a,if((a[x]^2)%n!=0&&a[(a[x]^2)%n]!=0,a[(a[x]^2)%n]=0));a=vecsort(a,,8);a[2]
(19:41)>?SOD
SOD(r)=c=eval(Vec(Str(r)));b=sum(X=1,#c,c[X])
(19:41)>m=vector(100,n,if(n==1,2,));for(x=2,100,m[x]=(x/2)+((x/2)+1));m

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Regarding Squares	a1call	Miscellaneous Math	42	2017-02-03 01:29
k*b^n+/-c where b is an integer greater than 2 and c is an integer from 1 to b-1	jasong	Miscellaneous Math	5	2016-04-24 03:40
A Sum of Squares Problem	MattcAnderson	Puzzles	7	2014-08-17 07:20
Representation of integer as sum of squares	kpatsak	Math	4	2007-10-29 17:53
squares or not squares	m_f_h	Puzzles	45	2007-06-15 17:46

2012-03-26, 21:08	#61
sascha77 Jan 2010 germany 2·13 Posts	I think the reason why a mersenne number can not expressed as the sum of two squared numbers, is shown in this pdf (On Page 2. Proposition 1) http://www.math.uga.edu/~pete/4400twosquares.pdf This is a proof, that NONE number n with the form: $n \equiv 3 \;(\;mod \;4\;)$ can be expressed as sum of two squares. But every mersenne number has this form. $2^p \equiv 0 \;(\;mod \;4\;)$ -> $2^p-1 \equiv -1 \equiv 3 \;(\;mod\;4\;)$