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Subject: "x^2 + y^n = z^(2n)"     Previous Topic | Next Topic
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Boa Ben-David (Guest)
guest
Dec-30-00, 08:08 PM (EST)
 
"x^2 + y^n = z^(2n)"
 
   Hi Alex,

I wonder if you happened to know whether the expression
x^2 + y^n = z^(2n) was ever addressed. x,y,z integers, n is odd >= 3

I found, on the net x^2 + y^3 = z^6

---- www.seanet.com/~ksbrown/kmath213.htm

I asked people to run numbers for counter example and nil was found up to n=20.

Obviously, the claim is that no non-trivial solutions exist. So far I failed to prove it and so failed some gifted I have asked to try. Yet, some strong indications exist to support the
claim/hypothesis/conjuncture.

Please note, I am not even an amateur.

Boaz Ben-David.

p.s
in one of your marvelous pages you wrote "enough to the wise"
the original saying, which looks to fit better, is: "enough to the wise with a hint"



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  Subject     Author     Message Date     ID  
  RE: x^2 y^n = z^(2n) alexb Dec-30-00 1
     RE: x^2 y^n = z^(2n) Boa Ben-David (Guest) Jan-01-01 2
         RE: x^2 y^n = z^(2n) alexb Jan-01-01 3
             RE: x^2 y^n = z^(2n) Boa Ben-David (Guest) Jan-01-01 4
                 RE: x^2 y^n = z^(2n) alexb Jan-01-01 5
                     RE: x^2 y^n = z^(2n) Boa Ben-David (Guest) Jan-01-01 6

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alexb
Charter Member
672 posts
Dec-30-00, 08:13 PM (EST)
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1. "RE: x^2 y^n = z^(2n)"
In response to message #0
 
   Dear Boaz:

I wonder if you happened to know
whether the expression
x^2 + y^n = z^(2n) was ever addressed.
x,y,z integers, n is odd >=3

No, I can't say anything about it. I would post a question like this to the sci.math newsgroup. There's a recent thread on Beal's conjecture, so there must be people out there who may help you with your question. Here's a short page on Beal's conjecture:

www.maa.org/devlin/devlin_12_97.html

in one of your marvelous pages
you wrote "enough to the wise"
the original saying, which looks
to fit better, is: "enough to the
wise with a hint"

For me, the beauty of the Hebrew saying is in its compactness. Of course, there's an implied background, a view point annunciated just beforehand. Which presumably should suffice for the wise all by itself. "Vedai lehaham" is just an extended period which a haham should not need. To say that the above background is a hint to a deeper meaning is to deny that it's addressed to a haham.

But of course I may be mistaken.

Thank you for the kind words.

All the best,
Alexander Bogomolny


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Boa Ben-David (Guest)
guest
Jan-01-01, 01:21 AM (EST)
 
2. "RE: x^2 y^n = z^(2n)"
In response to message #1
 
   Dear Alex,
Thanks for your express reply.

> I wonder if you happened to
> know whether the expression
> x^2 + y^n = z^(2n) was ever addressed.
> x,y,z integers, n is odd >=3

No, I can't say anything about it.
I would post a question
like this to the sci.math newsgroup.

I did. Though in another form. Yet, with a 100$ prize offer and a bonus for extra $100. No one collected the prize. Only one reply was mailed, without much help.

If you "can't say anything about it" what does that mean? What are the kind of mathematicians I should look after? Can you suggests names?

There's a recent thread
on Beal's conjecture, so there
must be people out there who
may help you with your question.

How do I pick the right people from within a thread, without getting entangled with non-proper people? I run into the Beal's conjuncture. Also to Catalan's. Thanks.

> in one of your marvelous pages
> you wrote "enough to the wise"
> the original saying, which looks
> to fit better, is: "enough to the wise
> with a hint"

For me, the beauty of the Hebrew
saying is in its compactness.

I thought this is what you had in mind. When you use a saying, it is very hard to shorten it, without loosing its taste. Just like in poetry. Remember, it was filtered by the best filter. Time itself. In this case, about 2000 years.

Of course,
there's an implied background, a
view point annunciated just beforehand.
Which presumably should suffice for
the wise all by itself. "Vedai lehaham"

The original saying is: "vedai lechachima birmiza" Assuming you know Hebrew, your quote, change the meaning of the saying. I am not sure even if it's grammar is correct.

is just an extended period which a
haham should not need.

Ah, you got the saying wrong.

To say that the
above background is a hint to a
deeper meaning is to deny that it's
addressed to a haham.

It doesn't say anything on any background. The saying just say that for a wise guy, a hint is enough. Obviously, the saying is not addressed to the wise. It is just another saying _on_ wise guys which should be classified as "how would some one know who is the wise" Among that list would be: "The one that can forcast the born", etc'.

Thank you for the kind words.

It was underestimate.
A real beauty.
Keep going.

Boaz



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alexb
Charter Member
672 posts
Jan-01-01, 01:23 AM (EST)
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3. "RE: x^2 y^n = z^(2n)"
In response to message #2
 
   Boa Ben-David wrote:

If you "can't say anything about
it" what does that mean?

That I know nothing about it. Just outside my interests and
expertise, if any.

How do I pick the right people
from within a thread, without getting
entangled with non-proper people?

I do not know. May there be a special discussion group with focus
on number theory?

The original saying is: "vedai
lechachima birmiza"
more, it is still short ]
Assuming you know Hebrew,

I am an Israeli from 1974.

your quote, change the meaning of the saying.
I am not sure even if it's grammar is correct.

I am sure that given time I'll be able to point you to several
pages in Talmud where the saying appears just as "vedai lhaham."

I do not know where the original saying comes from.

> is just an extended period
> which a haham should not need.
Ah, you got the saying wrong.

Well. I do not think so.

> To say that the
> above background is a hint to
> a deeper meaning is to deny that it's
> addressed to a haham.

It doesn't say anything on any background.
The saying just say that for a wise guy, a hint is enough.
Obviously, the saying is not addressed to the wise.

The saying is addressed to a reader. As I said, it often
appears in talmud in the short version. It'says nothing
of the background, but just terminates some words of wisdom.

You may want to check this with a rabbi in your neighborhood.

All the best,
Alexander Bogomolny


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Boa Ben-David (Guest)
guest
Jan-01-01, 10:19 AM (EST)
 
4. "RE: x^2 y^n = z^(2n)"
In response to message #3
 
   The saying is addressed to a
reader. As I said, it often
appears in Talmud in the short
version. It'says nothing
of the background, but just
terminates some words of wisdom.

You may want to check this with a
rabbi in your neighborhood.

You raised my curiosity.

Can we settle on my father's CD which contains about 400 searchable books, including the Bible,Talmud, Gmara, Rashi, etc. ? A Rabbi is not available to me.

OK. My father found 37 hits "vedai lechacham" in the CD. All 37 from the "SHO"T" = She'elot ve-tshuvot all 37 from the last 200 hundred years. Note: "vedai lechachima birmiza" is in Aramith and probably much older then 1800 AC.

For more details you will have to wait until I'll do the search by myself.For the moment, I withdraw from my remark.

Boaz



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alexb
Charter Member
672 posts
Jan-01-01, 10:21 AM (EST)
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5. "RE: x^2 y^n = z^(2n)"
In response to message #4
 
   Note: "vedai lechachima birmiza"
is in Aramith and probably
much older then 1800 AC.

The saying I suspect is very old. We may settle on that it was well known letana'im, who referred to it in its short form as there was no reason to write all of it.

This is the best I can do to reconcile the difference. However, if this is true then still, they could not use unless their was an assumed background. Usually there would be a story whose moral was not enunciated explicitly. Instead it would end in "vedai lechacham".

For more details you will have
to wait until I'll do the search by myself.
For the moment, I withdraw from my remark.

OK.

Best,
Alexander Bogomolny


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Boa Ben-David (Guest)
guest
Jan-01-01, 10:26 AM (EST)
 
6. "RE: x^2 y^n = z^(2n)"
In response to message #5
 
   background. Usually there would
be a story whose moral was not enunciated
explicitly. Instead it would end in
"vedai lechacham".

Just like in math.
A -> B and "vedai lechacham" B.
Hence the math is assumed as a background.
Usually many theorems are assumed as a "context background."
I accept the reconcilation

Best regards

Boaz


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