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Unformatted text preview: ence f ( x ) 0( p ) has n solutions a 1 , a 2 , . . . , a n mod p . Show that there is an integer polynomial q ( x ) such that the congruence f ( x ) ( x-a 1 )( x-a 2 ) ( x-a n ) q ( x )( p ) holds for each integer. Exercise 4. 2.7.6: Show that Theorem 2.26 becomes false when mod p is replaced by mod m where m is a composite number. Exercise 5. 2.7.10: Let p be an odd prime and write the rational number 1 1 + 1 2 + 1 3 + + 1 p-1 as a fraction a b reduced to lowest terms, i.e., ( a, b ) = 1. Show that p divides evenly into a ....
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This note was uploaded on 04/05/2010 for the course CS 150 taught by Professor Humphreys,g during the Spring '08 term at UVA.
- Spring '08