##### Department of Mathematics,

University of California San Diego

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### Math 295 - Colloquium

## Jack Sonn

#### Technion, Haifa, Israel

## Irreducible polynomials which are reducible locally everywhere

##### Abstract:

There exists a polynomial $f(x)$ of degree $n$ with integer coefficients which is irreducible over the rationals but reducible modulo $p$ for all primes $p$ if and only if $n$ is not a prime number. The same result holds with "reducible mod $p$" replaced by "reducible over $Q_p$", and generalizes to arbitrary global fields. (Joint work with Bob Guralnick and Murray Schacher)

Host: Adrian Wadsworth

### January 13, 2005

### 3:00 PM

### AP&M 6438

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