
Re: Cute question about polynomials
Posted:
Apr 25, 2014 9:28 PM


Pubkeybreaker wrote: > On Wednesday, April 23, 2014 11:26:46 PM UTC4, david petry wrote: >> On Tuesday, April 22, 2014 10:33:03 PM UTC7, Math Lover wrote: >>> Find a polynomial p(x,y) with real coefficients, such >>> that as x,y range over all the real numbers, the set >>> of values p(x,y) covers the entire interval (0,infinity}
>>I believe this to be true: this was a Putnam exam problem one >>year, and *nobody* got the answer!
> It should not be that difficult. Consider f(x,y) = epsilon, [...]
I agree that the problem is not very difficult, if you're told that such a polynomial does exist! The Putnam exam problem asked the question of whether such a polynomial exists, which is only a little bit different from the question "Math Lover" asked, but it's enough of a difference to make it much harder (for undergraduates, anyways). I was told by a source I consider to be very reliable that no one got the answer, which is indeed amazing, since some of the top guys taking the Putnam exam are rather sharp.

