# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 73: Eisenstein’s Criterion

December 24, 2016

Posted by on **Eisenstein’s criterion** provide a sufficient (but not necessary) set of criterion for a polynomial with integer coefficients

to be irreducible over the rationals. The criterion are that there exists a prime such that

- divides where
- doesn’t divide
- doesn’t divide

If all these conditions are true, then can’t be reduced over the rationals.

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