Problem 420

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jpatou
Posts: 9
Joined: Sat Mar 09, 2013 8:13 am

Problem 420

Post by jpatou » Sun Mar 24, 2013 5:30 pm

I've got a problem for this one : I find F(50) = 6 with these matrix
[5, 4]
[4, 5]

[10, 6]
[6, 10]

[17, 8]
[8, 17]

[20, 8]
[32, 20]

[20, 32]
8, 20]

[20, 16]
[16, 20]

Can someone check if these are correct and if so, which one I missed ?
Thanks
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Ted
Posts: 19
Joined: Sun Apr 02, 2006 9:46 pm

Re: Problem 420

Post by Ted » Sun Mar 24, 2013 10:32 pm

These look correct.
The trace of the missing one is 26.
Good luck!

jpatou
Posts: 9
Joined: Sat Mar 09, 2013 8:13 am

Re: Problem 420

Post by jpatou » Mon Mar 25, 2013 12:12 pm

Thanks very much .
I identified and fixed the bug. My function to test matrix candidates now works.
Now I have to think how to eliminate quickly most of the candidates.
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3uc1id
Posts: 3
Joined: Wed Mar 27, 2013 10:13 pm

Re: Problem 420

Post by 3uc1id » Wed Mar 27, 2013 10:19 pm

I actually computed 8 different matrices for F(50)!! Which is a liar?

[5 4]
[4 5]

[10 6]
[6 10]

[13 12]
[12 13]

[17 8]
[8 17]

[12 8]
[24 28]

[20 8]
[32 20]

[20 16]
[16 20]

[18 9]
[18 27]

RobA
Posts: 7
Joined: Sat Mar 23, 2013 11:00 pm

Re: Problem 420

Post by RobA » Wed Mar 27, 2013 10:32 pm

This same list of eight matrices is given in a math.stackexchange post http://math.stackexchange.com/questions ... -euler-420. That post also gives the square roots and those square roots are not all positive integer matrices.

3uc1id
Posts: 3
Joined: Wed Mar 27, 2013 10:13 pm

Re: Problem 420

Post by 3uc1id » Wed Mar 27, 2013 10:34 pm

yeah, that post was me :p i didn't realize that 0 wasn't positive

3uc1id
Posts: 3
Joined: Wed Mar 27, 2013 10:13 pm

Re: Problem 420

Post by 3uc1id » Tue May 21, 2013 10:02 pm

Does the answer to this fit in a C unsigned long int?

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TheEvil
Posts: 84
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Location: Szeged, Hungary

Re: Problem 420

Post by TheEvil » Wed May 22, 2013 6:52 am

Yes.
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Jochen_P
Posts: 50
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Location: Stuttgart, Germany

Re: Problem 420

Post by Jochen_P » Fri Nov 16, 2018 9:02 am

I don't get this at all.. Can someone explain to me how these matrices relate to each other?
The sum of those matrices are different and I just can't make out any other relation :oops:

taking the sample:
Image

Maybe I'm just a bit undercaffeinated?
Image

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hk
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Re: Problem 420

Post by hk » Fri Nov 16, 2018 9:16 am

Squaring a matrix has nothing to do with matrix addition.
What you can read there is that for some matrices A,B,C holds that $A=B^2$ but also $A=C^2$
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Jochen_P
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Location: Stuttgart, Germany

Re: Problem 420

Post by Jochen_P » Fri Nov 16, 2018 9:33 am

Nope, sorry.
Still don't get it. Seems that I'm a bit thick today :(

[edit] The only thing I see there is that the ratios on the diagonals are the same in every matrix, but how that accounts for those lesser matrices to be squared? No clue[/edit]

[edit 2] Animus was so kind to link me to the corresponding wiki article, Thanks [/edit]
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RobertStanforth
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Re: Problem 420

Post by RobertStanforth » Fri Nov 16, 2018 10:02 am

To be clear: 'squaring' a matrix refers specifically to matrix multiplication of a matrix with itself.

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