Unformatted text preview: 5. The Chinese Remainder Theorem (Thm. 2.18 in NZM) 6. Hensel’s Lemma (Thm. 2.23 in NZM) 7. Solutions to f ( x ) mod p are bounded by deg( f ) (Thm. 2.26 in NZM) 8. f ( x ) has deg( f ) solutions if and only if it divides x px mod p (Thm. 2.28 in NZM, you may assume the previous result in proving this theorem.) 9. Condition on solutions to x n ≡ a mod p (Thm. 2.37 in NZM) 10. There exist φ ( p1) primitive roots mod p (NZM Thm. 2.36 – you may assume elementary facts about the order of an element, e.g. Lemmas 2.33 and 2.34 in NZM) 11. Gauss’ Lemma (Thm 3.2 in NZM)...
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 Spring '09
 BRUBAKER
 Number Theory, Linear Congruence Theorem, NZM, primitive roots mod

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