Number 59649589127497217 is a factor of Fermat number F7 - Page 4

literka · 2013-11-16, 02:30

Quote:

Originally Posted by Batalov

Here's how one "scratches left ear with the left hand".
(All you need is a pencil and one sheet of paper for up to F7 and if your handwriting is neat enough, with space to spare for the F8.)

Code:

Lemma 5A. 641 divides 2^32+1.
Proof: 2^8 = 256. 
Let's square this value two more times modulo 641, and compare to 641-1.
(256^2)%641 = 154
(154^2)%641 = 640. QED.

Lemma 6A. 274177 divides 2^64+1.
Proof: 2^16 = 65536. 
Let's square this value two more times modulo 274177, and compare to 274177-1.
(65536^2)%274177= 258768.
(258768^2)%274177= 274176. QED.

Lemma 7A and so on. Same thing over and over again.

And you started to behave like a high school student again. Don't you see the difference between these proofs and my proofs or a proof presented by jyb (quoted from Wikipedia)?

retina · 2013-11-16, 02:38

Quote:

Originally Posted by ewmayer

I have through exhaustive labors succeeded in verifying part 2 of my proof by dilemma. We first tabulate multiples of the larger (purported) multiplicand by 0-9: 5704689200685129054721 x ____ =

Code:

0	                      0
1	 5704689200685129054721
2	11409378401370258109442
3	17114067602055387164163
4	22818756802740516218884
5	28523446003425645273605
6	34228135204110774328326
7	39932824404795903383047
8	45637513605481032437768
9	51342202806166161492489

And here is the resulting (no FFTs, DWTs or other suspicious 3-letter-initialism-denoted computer flummery allowed here) multiplication rhombus, with blank spaces denoting 0s. Columnwise addition gives - someone please double-check my carries! - the indicated sum, matching the desired result:

Code:

59649589127497217 x 5704689200685129054721:

5:   28523446003425645273605
9: +  51342202806166161492489
6: +   34228135204110774328326
4: +    22818756802740516218884
9: +     51342202806166161492489
5: +      28523446003425645273605
8: +       45637513605481032437768
9: +        51342202806166161492489
1: +          5704689200685129054721
2: +          11409378401370258109442
7: +           39932824404795903383047
4: +            22818756802740516218884
9: +             51342202806166161492489
7: +              39932824404795903383047
2: +               11409378401370258109442
1: +                 5704689200685129054721
7: +                 39932824404795903383047
--------------------------------------------
Sum= 340282366920938463463374607431768211457
[Nonzero Carries as noted:
     11112332345456777777886775664432332    ]

Whew! I need a beer. Lemma 1 may need to wait a few days. Hey, even Hercules [or "Herakles" to the OP] needed to rest between his famous labors, I'll bet.

You are so clever. You deserve a cookie young man. Ever thought about becoming a minion?

Batalov · 2013-11-16, 02:57

Quote:

Originally Posted by Batalov

literka,

Could you please present the number of operations needed to carry on all your calculation (1) - (5), etc, compared to a simple multiplication of two factors.

It appears that to assert these:

Code:

Several equalities will be needed:

(1)                          p=208648999^2+126945596^2 = 512 * q+1

(2)                          s = 208648999*52542249 + 126945596*31967597

(3)                          126945596*52542249 - 208648999*31967597 = 1

(4)                         309*q + r = 2^55

(5)                         r = (s div 512)+1

one will have to do much more ...

Write (1) through (5) for us

Quote:

Originally Posted by literka

...with no help of a computer and avoid time-consuming computations as presented by Retina.
In mathematics something computed by a computer is not regarded as a proof.

Now, by your own standards: Write these calculations out for us like we did for you. Show us 208648999*52542249, show us 208648999*31967597, "prove" that 126945596*52542249 - 208648999*31967597 = 1. Don't be lazy. No computers. Then, 208648999*52542249 + 126945596*31967597, and show that this is equal to s.

Then compare to simple squaring.

literka · 2013-11-16, 03:19

Quote:

Originally Posted by Batalov

Write (1) through (5) for us

Now, by your own standards: Write these calculations out for us like we did for you. Show us 208648999*52542249, show us 208648999*31967597, "prove" that 126945596*52542249 - 208648999*31967597 = 1. Don't be lazy. No computers. Then, 208648999*52542249 + 126945596*31967597, and show that this is equal to s.

Then compare to simple squaring.

Why should I do it for you, after you ridiculed my proofs? Read what I wrote on my webpage. These numbers are large, but very small in comparison with F7. Your "simple" squaring would give you a number comparable with F7;
My idea is such: if someone does not want to understand, leave him alone because any effort is hopeless.

Batalov · 2013-11-16, 03:47

Suit yourself, because by doing this you simply admit that you failed by your own standard.

If you paid close attention, you would find that the message that I quoted was my first post; it was a question that I asked you from the very start and you didn't answer; so I simply reminded you; it has nothing to do with whether you felt ridiculed or not. The second quote is also fully in context and in it, you explain the purpose of your "proof". That particular purpose is completely failed, because you cannot demonstrate (1) through (5) with less computational* effort than the straightforward computation is worth.

As to your last point, it is very important to periodically look in the mirror.

Anyway, Don, stop the charade and re-login as yourself. ;-)

_______
*computational in broad sense, that is, down to earth: with pencil and paper.

literka · 2013-11-16, 04:21

Quote:

Originally Posted by Batalov

Suit yourself, because by doing this you simply admit that you failed by your own standard.

If you paid close attention, you would find that the message that I quoted was my first post; it was a question that I asked you from the very start and you didn't answer; so I simply reminded you; it has nothing to do with whether you felt ridiculed or not. The second quote is also fully in context and in it, you explain the purpose of your "proof". That particular purpose is completely failed, because you cannot demonstrate (1) through (5) with less computational* effort than the straightforward computation is worth.

As to your last point, it is very important to periodically look in the mirror.

Anyway, Don, stop the charade and re-login as yourself. ;-)

_______
*computational in broad sense, that is, down to earth: with pencil and paper.

Imagine that I do not have obligation to answer all your questions, especially those, which require lot of work to answer. I still remember your unfair behavior with respect to me. You did not write posts to me, but behind my back, but I read them. Why do you think that this has nothing to do with my answering to your posts? Well, I still want to be polite and I answer your posts, but I should not do it. You have 2 choices: to accept my proofs or reject them. I do not care what you will do.

c10ck3r · 2013-11-16, 05:37

Quote:

Originally Posted by literka

Imagine that I do not have obligation to answer all your questions, especially those, which require lot of work to answer. I still remember your unfair behavior with respect to me. You did not write posts to me, but behind my back, but I read them. Why do you think that this has nothing to do with my answering to your posts? Well, I still want to be polite and I answer your posts, but I should not do it. You have 2 choices: to accept my proofs or reject them. I do not care what you will do.

Imagine that members of this forum know "ein bissyen" of mathematics, and can recognize within seconds that your proofs are rehashing known results using more effort than would be required by any one of several methods. Throughout this thread you have disregarded the advice of computer science professionals and mathematicians as they attempted to point this out to you. Your first sentence in this quote references questions "which require lot of work to answer" (sic) seems, to members of this forum especially, as rather counter-intuitive given the amount of work you put in to prove that a known factor is indeed a known factor. There have been a number of occasions in which you have posted statements as fact and have had them disproven by professionals in the field, and yet you refuse to see this.
If you feel that you have been disrespected on this forum, you may go elsewhere, if you are so inclined. Otherwise, if you wake up and recognize that the people that have responded have been making valid points the entire time, and get the urge to learn why your proof is, for all practical purposes, pointless, feel free to ask logical questions and to take the advice of the senior members of this forum. Also, if Robert Silverman, CRGreathouse, WBlipp, Batalov, et al. suggest reading a certain paper, DO SO! Comprehension of the sources will usually provide an understanding of why certain things work or don't work in mathematics, and how to apply them.

LaurV · 2013-11-16, 06:10

You guys are geniuses! You made my day. What I say my day? You made my whole weekend!

Few brilliant quotes in this thread, which would be a pity to be lost. If you think about the context, they are even more beautiful.

Quote:

Originally Posted by retina

I considered making him do it in hexadecimal just to show that he understood how hex works but somehow that seemed a little bit too cruel even for me.

To this, I could not stop laughing, considering also the context and where is coming from, but to the next one I almost had a cardiac failure, felt down to my bottom, and is still painful,

Quote:

Originally Posted by literka

<to RDS, (this is important!): > I read your book, but only to check the level of your mathematics.

(the words in the slicers are mine, that was an important mention to do, it would not be so funny if he would be telling it to me, for example). I imagine myself going to my sensei, provoking him to a fight, and saying that I want to test his skills. Real stuff, I am not invented anything, the man was Moroccan, 1.95 tall, 120kg, no fat, imagine Hulk Hogan young and blacker, he was studying medicine in my country in the seventies, and making some sunday money by teaching children like I was how to defend themselves. He was a wonderful person, very good in his branch (world class!) and very kind with us, but if I would go to him and do what I just said, I may not be able to post on this forum for a while, hehe...

Quote:

Originally Posted by Batalov

Alleged added value of the "proof": it operates only with numbers no more than 2. While direct multiplication deals with larger numbers (i.e. 3).

Quote:

Originally Posted by literka

My idea is such: if someone does not want to understand, leave him alone because any effort is hopeless.

RIGHT! BINGOOOOO! However, lot of clever people here waste precious time trying to make you understand, I don't get it why? Behaving like a log is an innate behavior.

Quote:

Originally Posted by literka

You did not write posts to me, but behind my back, but I read them.

(note that the posts were on a public forum, but not directly addressed to the literka thing, like I sometime write things of the type "I like/I don't like Batalov, but don't tell him",

)

Let me add my wondering question markto this:

Quote:

Originally Posted by Batalov

On to the same Herculean task for F8, then? Is it already in the plans?

------------------
Well, I have a smell for cranks. (That is because I am a kinda crank myself, and the thieves usually can smell each other, but don't tell this to anyone). I am most probably in his ignore list, after I was "treating him like he was a thing, and not a living person" when he started posting here (to which the same people in this thread jumped on my head! I bet they feel sorry now

). But this literka guy (whoops! I just did it again!) is one of the dangerous type. There are many types of cranks, some are innocents, or childish, like cmd was, or genuine clowns, like don ablaze, but there also is that type of proud idiot who really believe in what he does, and believe all people around him are stupid because they don't understand what he is doing, and because they don't approve him and don't raise him on their arms. This type of guy is more dangerous if he is teaching is some elementary or gymnasium school somewhere, because he destroys the lives of many innocent children....

jyb · 2013-11-16, 07:43

Quote:

Originally Posted by Batalov

Anyway, Don, stop the charade and re-login as yourself. ;-)

Now, now. While everyone seems to agree that literka's manipulations don't have much value, they at least appear to be valid. DB clearly lacked the necessary knowledge of mathematics to even get that far. Still, he made up for it with some wonderful delusions of grandeur.

literka · 2013-11-16, 08:39

Quote:

Originally Posted by LaurV

(That is because I am a kinda crank myself, and the thieves usually can smell each other, but don't tell this to anyone).

This if very truth. But don't worry I won't tell it to anybody. Only the word "kinda" doesn't match.

literka · 2013-11-16, 08:41

Quote:

Originally Posted by jyb

Now, now. While everyone seems to agree that literka's manipulations don't have much value.

Where is this information from?

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2013-11-16, 03:47	#38
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²·7·331 Posts	Suit yourself, because by doing this you simply admit that you failed by your own standard. If you paid close attention, you would find that the message that I quoted was my first post; it was a question that I asked you from the very start and you didn't answer; so I simply reminded you; it has nothing to do with whether you felt ridiculed or not. The second quote is also fully in context and in it, you explain the purpose of your "proof". That particular purpose is completely failed, because you cannot demonstrate (1) through (5) with less computational* effort than the straightforward computation is worth. As to your last point, it is very important to periodically look in the mirror. Anyway, Don, stop the charade and re-login as yourself. ;-) _______ *computational in broad sense, that is, down to earth: with pencil and paper.