- Thread starter
- #1

- Mar 10, 2012

- 834

- Thread starter caffeinemachine
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- Thread starter
- #1

- Mar 10, 2012

- 834

- Thread starter
- #2

- Mar 10, 2012

- 834

Let $p(t)$ and $q(t)$ have a non trivial common factor in $K[t]$. Assume that $p$ and $q$ don't have a non-trivial common factor in

$F[t]$. Then there exist $a,b\in F[t]$ such that $pa+qb=1$. But this contradicts the fact that $p$ and $q$ have a non-trivial common factor in $K[t]$.