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#1 2006-09-08 10:42:55

Randompasserby
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I have a really hard question

here is the question...the smallest non-palindromic number whose square is a palindrome. if you can figure this out...i sure cant...i would love you forever!!

#2 2006-09-08 10:58:48

randompasserby
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Re: I have a really hard question

or if loving you forever scares you..i wont. thanks in advance!

#3 2006-09-08 11:11:10

MathsIsFun
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Registered: 2005-01-21
Posts: 7,711

Re: I have a really hard question

26


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2006-09-08 11:13:53

randompasserby
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Re: I have a really hard question

thanks so much!

#5 2006-09-09 06:29:27

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: I have a really hard question

Up to 100.000 there are 8 more:

264:69696

307:94249

836:698896

2285:5221225

2636:6948496

22865:522808225

24846:617323716

30693:942060249

It seems they are rare. Are there infinity of them?


IPBLE:  Increasing Performance By Lowering Expectations.

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#6 2006-09-09 12:25:50

randompasserby
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Re: I have a really hard question

probally.

#7 2006-09-09 12:54:43

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: I have a really hard question

I can't even begin to see how constructing such a proof would be possible.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#8 2006-09-09 13:01:38

randompasserby
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Re: I have a really hard question

me neither..but dont ask me im only in ninth grade

#9 2006-09-09 21:17:45

krassi_holmz
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Posts: 1,905

Re: I have a really hard question

I'm in eighth.
Such proofs involve fermat's little theorem and euler's theorem (for modulus).
And all the proves I have seen are constructive.
If we find a pattern for this numbers it will be easier.

Last edited by krassi_holmz (2006-09-09 21:26:45)


IPBLE:  Increasing Performance By Lowering Expectations.

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#10 2006-09-09 21:26:18

krassi_holmz
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Re: I have a really hard question

I'll try bigger.
I've written a nice program in Mathematica, but it's incredibly... slow sad.
I'll try with C program.


IPBLE:  Increasing Performance By Lowering Expectations.

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#11 2006-09-09 21:29:31

krassi_holmz
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Re: I have a really hard question

Up to 10^6 I have founded one more (with mathematica):
798644:637832238736


IPBLE:  Increasing Performance By Lowering Expectations.

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#12 2006-09-10 00:44:53

MathsIsFun
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Re: I have a really hard question

krassi_holmz wrote:

I'm in eighth.

So you are ... 14?

Ricky wrote:

I can't even begin to see how constructing such a proof would be possible.

We should give these numbers a name, then we can make a conjecture, then in 100 years someone can get the Fields Medal by proving our conjecture.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#13 2006-09-10 02:06:17

krassi_holmz
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Re: I have a really hard question

MathsIsFun wrote:
krassi_holmz wrote:

I'm in eighth.

So you are ... 14?

No I'm 16.

Ricky wrote:

I can't even begin to see how constructing such a proof would be possible.

We should give these numbers a name, then we can make a conjecture, then in 100 years someone can get the Fields Medal by proving our conjecture.

That's good. But it will be better if we find some connection with the Riemann's hypothesis. wink


IPBLE:  Increasing Performance By Lowering Expectations.

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#14 2006-09-10 02:08:48

krassi_holmz
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Registered: 2005-12-02
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Re: I have a really hard question

We can call them "Passerby" numbers...


IPBLE:  Increasing Performance By Lowering Expectations.

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#15 2006-09-10 02:13:28

krassi_holmz
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Registered: 2005-12-02
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Re: I have a really hard question

Sorry, I'll dissapoint you.
I've taught that becuse this numbers are interesting, they should have been investigated.
And I've founded them in the OEIS:
http://www.research.att.com/~njas/sequences/A016106


IPBLE:  Increasing Performance By Lowering Expectations.

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#16 2006-09-10 02:38:06

Ricky
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Re: I have a really hard question

My vote is for "Mirror squares"


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#17 2006-09-10 04:25:59

randompasserby
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Re: I have a really hard question

oh well im thirteen. and thanks! kudos!

#18 2006-09-10 04:32:01

randompasserby
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Re: I have a really hard question

so they are already called something?

#19 2006-09-10 04:33:36

randompasserby
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Re: I have a really hard question

oh they are not...so we need to decide on a name. any takers?wave

#20 2006-09-10 05:00:14

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: I have a really hard question

I'm for "passerby"!!!


IPBLE:  Increasing Performance By Lowering Expectations.

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#21 2006-09-10 05:03:17

krassi_holmz
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Registered: 2005-12-02
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Re: I have a really hard question

I don't think "mirror squares" is best, because we should name the numbers, not their squares.
But we can take 2 names - for example "passerby" for the numbers, and "mirror squares" for their squares.


IPBLE:  Increasing Performance By Lowering Expectations.

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#22 2006-09-11 10:13:33

randompasserby
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Re: I have a really hard question

our math teacher says that math people can be very unimaginable with names sometimes. (an insult in my opinon, but whatever.) so i am thinking lets go outside the box with something uniqe. how about....um....i cant really think of anything. lol. ok i guess im not creative. roflol
i like the passerby and mirror scuares idea. but any one get a little creative with the names?

#23 2006-09-12 00:26:15

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: I have a really hard question

"Creative"?
What do you mean?
(give an example of some "creative" names)


IPBLE:  Increasing Performance By Lowering Expectations.

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#24 2006-09-12 00:31:40

Ninja 101
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Registered: 2006-02-20
Posts: 936

Re: I have a really hard question

Palindrome? palin-track?


Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized.

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#25 2006-09-15 11:55:13

randompasserby
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Re: I have a really hard question

i dont know...as i said im not creative. but i must prove my math teacher wrong!!!

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