# Hw6 - Math 55 Homework 6 Due Friday Directions You should work on these problems and write up solutions in groups of two Your answer should be

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Math 55 - Homework 6 Due Friday, July 22, 2011 Directions: You should work on these problems and write up solutions in groups of two . Your answer should be clear enough that it explains to someone who does not already understand the answer why it works. (This is diﬀerent than just convincing the grader that you understand.) 1. Polynomials mod p . In this problem: p is a prime. all polynomials have integer coeﬃcients. Deﬁnitions: For polynomials f ( x ) = a k x k + ... + a 1 x + a 0 and g ( x ) = b k x k + ... + b 1 x + b 0 , we say that f ( x ) g ( x )(mod p ) if for every i , a i b i (mod n ). For a polynomial f ( x ) = a k x k + a k - 1 x k - 1 + ... + a x + a 0 , deﬁne deg p ( f ) to be the largest integer (at most k ) so that p 6 | a deg p ( f ) (and deg p ( f ) = -∞ if no such integer exists.) (a) If f ( x ) g ( x )(mod p ), and m is an integer, prove that f ( m ) g ( m )(mod p ). (b) Prove the for any polynomial

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## This note was uploaded on 03/14/2012 for the course MATH 55 taught by Professor Strain during the Summer '08 term at University of California, Berkeley.

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Hw6 - Math 55 Homework 6 Due Friday Directions You should work on these problems and write up solutions in groups of two Your answer should be

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