##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Taylor Dupuy

#### UCLA

## "Linear" Constructions with Nonlinear Fermat Quotient Operators

##### Abstract:

The integers do not admit any nontrivial derivations. We will explain how the operation $x \to$ ${x-x^p \over p}$ can be thought of as a replacement for the derivative operator on the integers. After the introduction we hope to explain some recent work on the meaning of "linearity" in this theory.

Host: Kiran Kedlaya

### November 7, 2013

### 12:00 PM

### AP&M 7321

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