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Unformatted text preview: example: a = 3 , b = 4 , c = 0. (6) Problem 16 ii on page 77. Solution: Note that 68 2 mod 7. So we have 68 105 (2) 105 ((2) 3 ) 35 (8) 35 (1) 53 1 mod 7. (7) Problem 18 on page 78. Solution: Note that 6 5 mod 11. If e is odd, we have 5 e + 6 e 5 e + (5) e 5 e5 e 0 mod 11. If e is even, say e = 2 k , we have 5 e + 6 e 5 2 k + (5) 2 k 5 2 k + 5 2 k 2 5 2 k mod 11. So the question becomes: Does there exist an integer n such that 2 5 2 k = 11 n ? The answer is clearly no, since the right side has 11 in its prime factorization and the left side doesnt. 1...
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This note was uploaded on 09/05/2011 for the course MATH 3360 taught by Professor Billera during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 BILLERA
 Algebra

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