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Re: Cute question about polynomials
Posted:
Apr 25, 2014 9:28 PM
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Pubkeybreaker wrote:
> On Wednesday, April 23, 2014 11:26:46 PM UTC-4, david petry wrote:
>> On Tuesday, April 22, 2014 10:33:03 PM UTC-7, 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.
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