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Fermat's math problem ...

Started by florin91 , Aug 17 2011 11:34 AM

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#1 florin91

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Posted 17 August 2011 - 11:34 AM

English:
"I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain."

French:
"J'ai trouvé une merveilleuse démonstration de cette proposition mais ce doodle est trop étroit pour la contenir"

Portuguese
"Acabo de descobrir uma maravilhosa prova deste teorema, sendo que este doodle é demasiado pequeno para a demonstrar."

Italian
"Dispongo di una meravigliosa dimostrazione di questo teorema, ma questo doodle è troppo piccolo per contenerla."

German
"Ich habe hierfür einen wahrhaft wunderbaren Beweis gefunden, doch ist dieses Doodle zu schmal, um ihn zu fassen."

Spanish
"He descubierto una demostración verdaderamente maravillosa para este teorema pero este doodle es demasiado pequeño para contenerla."

Romanian
"Am descoperit o demonstraţie cu adevărat minunată pentru această teoremă, însă acest doodle este prea mic să o cuprindă."


Posted Image


It is impossible for a cube and a cube to give a cube,
or a fourth power and a fourth power to give a fourth power, or, more generally,
for any power of degree greater than two to be the sum of two powers of the given
degree.


In other words, x^n + y^n = z^n has no solution if n > 2 and if x, y, z are
required to be positive integers.

So, where is the demonstration?

A student once asked Wiener to solve a problem for him, so Wiener thought for a few moments and wrote down the answer. Now what the student really wanted was an explanation of the solution method, so he politely asked Wiener if there was some other way of doing the problem. Wiener thought again, smiled and said, "Yes, there is," and wrote down the answer again.


Now, an easier one: Could you find let's say, 1000 Pythagorean triples (a,b,c) so that a^2+b^2=c^2 ?
Post the method /source code of how you found them, how you generated them.
If it's possible, in more than one programming language.

Examples: (3,4,5); (5,12,13).

Source: www.google.com

@HS: This thread might not be the one you expect in this category, also known as a ctf challenge. If so, feel free to delete it, or do whatever you want, I don't mind :)

#2 Holmes.Sherlock

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Posted 17 August 2011 - 04:19 PM

Now, an easier one: Could you find let's say, 1000 Pythagorean triples (a,b,c) so that a^2+b^2=c^2 ?

Are you asking for exactly 1000 triplets or ANY number of triplets? What I can think is, if it's at all possible, the individual numbers will be so large that we'll need to create a separate number class, just like BigDecimal, to handle them. At the same time, I suspect if the solution were so easy, you wouldn't have posted it at all. :book:

#3 Wonko the Sane

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Posted 17 August 2011 - 04:49 PM

Are you asking for exactly 1000 triplets or ANY number of triplets? What I can think is, if it's at all possible, the individual numbers will be so large that we'll need to create a separate number class, just like BigDecimal, to handle them. At the same time, I suspect if the solution were so easy, you wouldn't have posted it at all. :book:



Have you actually read a bit on the topic? :dubbio: (I mean before theorizing to dedicate a class of numbers to them? :w00t:)

The question is to generate the the pitagorean triples and not their squares triples.

At first sight ;) finding 1,000 of them shouldn't be that difficult :whistling::
Spoiler


Excel (or any other spreadsheet) has more than enough precision to generate many more than 1000 of them.

:cheers:
Wonko

#4 Holmes.Sherlock

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Posted 17 August 2011 - 04:58 PM

Have you actually read a bit on the topic? :dubbio: (I mean before theorizing to dedicate a class of numbers to them? :w00t:)

I didn't have idea how big (or small) the numbers of 1000th triplets will be.

The question is to generate the the pitagorean triples and not their squares triples.

http://www.google.co...l0l0l0l0l0ll0l0

#5 pscEx

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Posted 17 August 2011 - 04:59 PM

Spoiler 


var

  num, num1: cardinal;

  a, b, c: cardinal;

  x, y, max: cardinal;

begin

  num := StrToInt(edit5.Text);

  num1 := 0;

  max := maxint;



  for y := 1 to max do

  begin

	for x := y + 1 to max do

	begin

  	a := x * x - y * y;

  	b := 2 * x * y;

  	c := x * x + y * y;

  	Inc(num1);

  	memo1.Lines.Add(IntToStr(num1) + ': ' + IntToStr(a) + ' ' + intToStr(B) + ' ' + IntToStr(c));

  	if num1 >= num then break;

	end;

	if num1 >= num then break;

  end;

end;
Peter :smart:

#6 Holmes.Sherlock

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Posted 17 August 2011 - 05:04 PM

@pscEx
Which language the above code is in?

#7 pscEx

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Posted 17 August 2011 - 05:06 PM

Delphi 7, the compiler which has been used for WinBuilder until current release.

Peter

@Wonko: I got the formula from http://www.mathe-lex...che-zahlen.html

#8 Holmes.Sherlock

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Posted 17 August 2011 - 05:09 PM

Delphi 7, the compiler which has been used for WinBuilder until current release.

:thumbsup: Possibly Nuno will soon come up with some Java code.

#9 pscEx

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Posted 17 August 2011 - 05:14 PM

... until current release.


:whistling:

Peter

#10 Holmes.Sherlock

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Posted 17 August 2011 - 05:20 PM

... until current release.

That's why I told. Isn't the latest one in Java?

#11 pscEx

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Posted 17 August 2011 - 05:20 PM

New version of "nativeEx_myPythagoras".

It delivers the 1000 "smallest" number triples.

Peter

var

  num, num1: cardinal;

  a, b, c: cardinal;

  x, y, max: cardinal;

begin

  num := StrToInt(edit5.Text);

  num1 := 0;

  max := maxint;

  for x := 1 to max do

  begin

	for y := 1 to x - 1 do

	begin

  	a := x * x - y * y;

  	b := 2 * x * y;

  	c := x * x + y * y;

  	Inc(num1);

  	memo1.Lines.Add(IntToStr(num1) + ': ' + IntToStr(a) + ' ' + intToStr(B) + ' ' + IntToStr(c));

  	if num1 >= num then break;

	end;

	if num1 >= num then break;

  end;

end;

#12 Wonko the Sane

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Posted 17 August 2011 - 05:21 PM

Comeon, you don't even need to calculate them:
http://www.tsm-resou...lists/trip.html

:cheers:
Wonko

#13 pscEx

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Posted 17 August 2011 - 05:22 PM

That's why I told. Isn't the latest one in Java?

Let's feel as childs before Christmas :innocent:

#14 pscEx

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Posted 17 August 2011 - 05:39 PM

Comeon, you don't even need to calculate them:
http://www.tsm-resou...lists/trip.html

:cheers:
Wonko

You gave an indirect link to 10000 triples.
As the forum does not accept this file as spoiler, here zipped: 19999 triples:
Attached File  nativeEx_Pythagoras.zip   257.42KB   1 downloads

Please understand, that I do not want to discuss, whether my app also can handle 20005, 31076 or any other number of triples!

Peter :rofl:

#15 Holmes.Sherlock

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Posted 17 August 2011 - 05:54 PM

Let's feel as childs before Christmas :innocent:

Children, I guess :dubbio:

#16 pscEx

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Posted 17 August 2011 - 06:30 PM

Maybe you are improving my English. I learned English at school only for one year. I think that you as "Historic-UK-Inhabitant" have English as second language.

Right now, IMO:
Children have parents, and they remain children of the parents for ever (maybe their age exceeds a certain number, that causes some people not to use the word 'children' any more).
Childs are very young people, maybe in the age before 10 or 12 or 14?

Peter

#17 Wonko the Sane

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Posted 17 August 2011 - 06:55 PM

Right now, (and at least since the 12th century AD ;)) children is the plural of child.
http://www.etymonlin....php?term=child

Maybe you were thinking of "kids"?

The "things" that "remain children of the parents forever" should be sons and daughters :dubbio:

:cheers:
Wonko

#18 pscEx

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Posted 17 August 2011 - 07:01 PM

Thanks, Ja.. Wonko for your explanation.

It has been much more helpful than every other posts I read the last minute.

Now I'm rather sure:

οἶδα οὐκ εἰδώς

Peter
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