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Topic: Cute question about polynomials
Replies: 63   Last Post: Apr 29, 2014 8:15 AM

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 David Petry Posts: 1,104 Registered: 12/8/04
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.

Date Subject Author
4/23/14 Math Lover
4/23/14 quasi
4/23/14 William Elliot
4/23/14 Math Lover
4/23/14 quasi
4/23/14 Port563
4/23/14 quasi
4/23/14 Port563
4/23/14 Peter Percival
4/23/14 Peter Percival
4/23/14 Port563
4/23/14 Jim Burns
4/23/14 Math Lover
4/23/14 Roland Franzius
4/23/14 Math Lover
4/23/14 Roland Franzius
4/23/14 Math Lover
4/23/14 Pfsszxt@aol.com
4/23/14 Math Lover
4/23/14 Peter Percival
4/23/14 Math Lover
4/23/14 ArtflDodgr
4/23/14 Math Lover
4/23/14 quasi
4/23/14 Math Lover
4/23/14 quasi
4/24/14 Richard Tobin
4/27/14 Port563
4/27/14 quasi
4/28/14 Port563
4/28/14 quasi
4/28/14 Port563
4/27/14 quasi
4/28/14 Port563
4/28/14 Leon Aigret
4/28/14 Port563
4/28/14 Bart Goddard
4/28/14 quasi
4/29/14 Leon Aigret
4/29/14 quasi
4/23/14 Port563
4/24/14 Roland Franzius
4/23/14 David Petry
4/24/14 Timothy Murphy
4/24/14 quasi
4/24/14 Math Lover
4/24/14 Port563
4/24/14 Math Lover
4/24/14 Port563
4/24/14 Math Lover
4/24/14 Jim Burns
4/24/14 Peter Percival
4/26/14 ross.finlayson@gmail.com
4/24/14 ross.finlayson@gmail.com
4/25/14 Math Lover
4/25/14 Port563
4/24/14 David Petry
4/24/14 Virgil
4/24/14 Port563
4/24/14 Virgil
4/24/14 Port563
4/25/14 Math Lover
4/25/14 Pubkeybreaker
4/25/14 David Petry

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