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Let $F$ be a field and $\langle a_1,...,a_n \rangle \subset F$.

Then given a non-zero polynomial $f \in F[X_1,...,X_n]$ is it true that if $f(a_1,...,a_n)=0$ then $(X_i - a_i)$ divides $f$ for some $i\leq n$?

  • 4
    This is one of those "almost any example is a counter-example" situations....2012-10-30
  • 1
    Consider $f(x,y)=(x-a)+(y-b), a,b\in F.$2012-10-30

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