#need help understanding this
stoic fableBOT
quartz prawn
Not sure but what if you assume x,y are integers then go through all the cases i.e. x,y are even | x even y odd | x odd y even | x, y odd
Then probably notice how the LHS and RHS are odd/even respectively and therefore can never be equal
I'm not sure! just my first thought
mint dagger
Can you explain what LHS and RHS are?? (im so sorry)
quartz prawn
Oh sorry. LHS is "left hand side" (of the equation). RHS is similar
I am also not sure if this works I am just solving it with you in a way 🙂
Just speaking my mind and trying ideas
quartz prawn
yeah go for it, just try something
I don't think my methodology will work btw :>
what kind of level of mathematics is this ? as in where did you find this question ?
mint dagger
what kind of level of mathematics is this ? as in where did you find this questi...
I don't know what level of mathematics is it but, I found it from google.
it's here: math.hkust.edu.hk/~yangwang/Misc/putnam_first100.pdf
remote epoch
I don't know what level of mathematics is it but, I found it from google.
it's...
the link wont work
remote epoch
oh thanks
civic ridge
do you want a hint?
||With imaginary numbers, you treat the real and imaginary part seperately because no real number will equal any imaginary number. You can do that with integers and sqrt(23), too. Also, a bunch of factoring that works for imaginary numbers work for integers and sqrt(23).||
lmk if that mkaes sense
makes*
worn escarp
||With imaginary numbers, you treat the real and imaginary part seperately becau...
Do you have a source for that? Quadratic extensions of Z being a UFD is a pretty nontrivial result to have
worn escarp
Okay, I did just go and check, if we assume Z[sqrt(23)] is a UFD then i have a proof
Let’s see if i can actually prove it is one or not
civic ridge
Let’s see if i can actually prove it is one or not
I thought it was on Wikipedia
I might be wrong
worn escarp
I can’t find it, mind sharing the link?
worn escarp
not that, we are talking about something else
civic ridge
Is the post in https://mathoverflow.net/questions/51667/for-which-c-is-mathbbz-sqrtc-a-unique-factorization-domain-a-euclide correct? If Lemmermeyer is right, then 23 = 3 mod 4 and is squarefree, so Z[sqrt(23)] is UFD.
worn escarp
Oh, cool, that’s a nice result I didn’t know
But surely there’s a less advanced proof of the question, it does say that it does not require an advanced math background
civic ridge
But surely there’s a less advanced proof of the question, it does say that it do...
It says most problems don't
Maybe we can look at some sort of mod residue?
worn escarp
It says *most* problems don't
Are we really gonna argue on semantics 😂
I’ll think about it