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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!!
or if loving you forever scares you..i wont. thanks in advance!
26
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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thanks so much!
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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probally.
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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me neither..but dont ask me im only in ninth grade
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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I'll try bigger.
I've written a nice program in Mathematica, but it's incredibly... slow .
I'll try with C program.
IPBLE: Increasing Performance By Lowering Expectations.
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Up to 10^6 I have founded one more (with mathematica):
798644:637832238736
IPBLE: Increasing Performance By Lowering Expectations.
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I'm in eighth.
So you are ... 14?
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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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.
IPBLE: Increasing Performance By Lowering Expectations.
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We can call them "Passerby" numbers...
IPBLE: Increasing Performance By Lowering Expectations.
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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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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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oh well im thirteen. and thanks! kudos!
so they are already called something?
oh they are not...so we need to decide on a name. any takers?
I'm for "passerby"!!!
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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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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.
i like the passerby and mirror scuares idea. but any one get a little creative with the names?
"Creative"?
What do you mean?
(give an example of some "creative" names)
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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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i dont know...as i said im not creative. but i must prove my math teacher wrong!!!