- #1
Euge
Gold Member
MHB
POTW Director
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Here's this week's problem!
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Problem: Suppose $p : \Bbb R^2 \to \Bbb R$ is a function of two variables $x$ and $y$ such that for every $x$, $p(x,y)$ is a nonzero polynomial in $y$, and for every $y$, $p(x,y)$ is a nonzero polynomial in $x$. Show that $p(x,y)$ is a nonzero element of $\Bbb R[x,y]$.
________Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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Problem: Suppose $p : \Bbb R^2 \to \Bbb R$ is a function of two variables $x$ and $y$ such that for every $x$, $p(x,y)$ is a nonzero polynomial in $y$, and for every $y$, $p(x,y)$ is a nonzero polynomial in $x$. Show that $p(x,y)$ is a nonzero element of $\Bbb R[x,y]$.
________Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!