Unformatted text preview: ence f ( x ) â‰¡ 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 ) â‰¡ ( xa 1 )( xa 2 ) Â·Â·Â· ( xa n ) q ( x )( p ) holds for each integer. Exercise 4. 2.7.6: Show that Theorem 2.26 becomes false when â€œmod p â€ is replaced by â€œmod m â€ 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 + Â·Â·Â· + 1 p1 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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 Spring '08
 Humphreys,G
 Prime number, ï¬ve lowest scores

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