PROBLEM OF THE MONTH
February 2006
Unfortunately, no one solved this problem :-((
Consider a polynomial p(x,y) in two variables with real coefficients.
Is it always true that there is a point (x0,y0) in the plane,
where the absolute value of this polynomial attains an absolute minimum
(i.e. in all other points (x,y), the absolute value of the polynomial is bigger or the same:
|p(x,y)| >= |p(x0,y0)|
)?
If yes, give a complete proof.
If no, give a counterexample.
This month's prize will be awarded to the best explained, correct solution.
Submit your solution to the Mathematics Undergraduate Office (Math P-142)
or electronically to
problem@math.sunysb.edu
by the due date. Acceptable electronic formats are: PDF, Postscript, DVI,
(La)TeX, or just plain text. Please include your name and phone number,
or preferably your email address.
Closing date: March 1st at 12 pm.