## Problem 420

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Comments, questions and clarifications about PE problems.

### Problem 420

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

[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

### Re: Problem 420

These look correct.

The trace of the missing one is 26.

Good luck!

The trace of the missing one is 26.

Good luck!

### Re: Problem 420

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.

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.

### Re: Problem 420

I actually computed

[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]

**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]

### Re: Problem 420

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.

### Re: Problem 420

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

### Re: Problem 420

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

### Re: Problem 420

Yes.

### Re: Problem 420

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

taking the sample:

Maybe I'm just a bit undercaffeinated?

The sum of those matrices are different and I just can't make out any other relation

taking the sample:

Maybe I'm just a bit undercaffeinated?

### Re: Problem 420

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 $A=C^2$

What you can read there is that for some matrices A,B,C holds that $A=B^2$ but also $A=C^2$

### Re: Problem 420

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]

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]

- RobertStanforth
- Administrator
**Posts:**839**Joined:**Mon Dec 30, 2013 11:25 pm

### Re: Problem 420

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