Unformatted text preview: example: a = 3 , b = 4 , c = 0. (6) Problem 16 ii on page 77. Solution: Note that 68 â‰¡ 2 mod 7. So we have 68 105 â‰¡ (2) 105 â‰¡ ((2) 3 ) 35 â‰¡ (8) 35 â‰¡ (1) 53 â‰¡ 1 mod 7. (7) Problem 18 on page 78. Solution: Note that 6 â‰¡ 5 mod 11. If e is odd, we have 5 e + 6 e â‰¡ 5 e + (5) e â‰¡ 5 e5 e â‰¡ 0 mod 11. If e is even, say e = 2 k , we have 5 e + 6 e â‰¡ 5 2 k + (5) 2 k â‰¡ 5 2 k + 5 2 k â‰¡ 2 Â· 5 2 k mod 11. So the question becomes: Does there exist an integer n such that 2 Â· 5 2 k = 11 n ? The answer is clearly â€œnoâ€, since the right side has 11 in its prime factorization and the left side doesnâ€™t. 1...
View
Full Document
 Spring '08
 BILLERA
 Algebra, Prime number, Integer factorization

Click to edit the document details