# Accession Number:

## ADA218148

# Title:

## Euler's Theorem for Polynomials

# Descriptive Note:

## Final rept. Aug 1988-Aug 1989

# Corporate Author:

## NAVAL RESEARCH LAB WASHINGTON DC

# Personal Author(s):

# Report Date:

## 1990-02-09

# Pagination or Media Count:

## 12.0

# Abstract:

The similarity of the arithmetic of the integers and the arithmetic of polynomials suggests that an analog of Eulers Totient theorem for integers also holds of polynomials over a finite field. This theorem is stated and proved, and then some properties of the totient function for polynomials are derived. The related notions of the order of one polynomials modulo another relatively prime polynomial, and of the exponent of a polynomial, are investigated. Finally, examples are given which show how to apply these ideas to the factorization of polynomials over finite fields.

# Descriptors:

# Subject Categories:

- Numerical Mathematics