Problem 420

[jpatou]

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

[Ted]

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

[jpatou]

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.

[3uc1id]

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]

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]

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

[3uc1id]

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

[TheEvil]

Yes.

[Jochen_P]

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?

[hk]

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 $A=C^2$

[Jochen_P]

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]

[RobertStanforth]

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

[mdean]

It might be a bit premature of me to ask, but when the problem says it can be expressed in 2 different ways, does it mean exactly 2 ways or at least 2 ways?

[heteroing]

It might be a bit premature of me to ask, but when the problem says it can be expressed in 2 different ways, does it mean exactly 2 ways or at least 2 ways?

If you're not sure, you should investigate the problem more. The correct interpretation will be clear with a bit of poking.