OK... if anyone is interested, see the original thread here. Hence an excellent ELSMO problem.

Does anyone have a full solution?

Can someone post a solution to this interesting problem? Thanks!

This is basically asking if there's 2 positive integers m and n such that each can be written as the sum of 2 positive squares in 2012 different ways, which is clearly true. Two such examples are found by raising 5 or 13 to any sufficiently large number

@above not quite. The question is asking whether there exist two positive integers $m$ and $n$ such that they can be written as a sum of 2 positive squares 2012 ways each such that there is a matching of the pairs where pairs that are connected share an element.

MathPanda1 wrote: Does anyone have a full solution?

MathPanda1 wrote: Does anyone have a full solution?

Seems like a hard problem -- No full solutions?

Bumb. Can't believe this has not been answered yet. (@MathFiFi I don't actually. The "can't believe" thing was not meant to be intimidating. It is a surprise that the post has over 2000 views and no one has posted a solution yet )

Hamel wrote: Bumb. Can't believe this has not been answered yet. do you know the answer? if so can you post it?

Can the creator at least shed some light upon this?

i think $m,n$ should be distince,otherwise we can pick $m=n$ and we need to find an integer $m$ such that $m$ can be written as sum of 2 squares in 2012 ways, which can easily proved by the identy $(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2$

Hamel wrote: Can the creator at least shed some light upon this? common sense much? lol 2012, y'think hes active on aops??

Math-Ninja wrote: Hamel wrote: Can the creator at least shed some light upon this? common sense much? lol 2012, y'think hes active on aops?? im assuming David Yang is the creator, not the OP

There was already a full solution posted in #2, you just have to follow the link. Here it is again.