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Unformatted text preview: x 9 (mod 11) is the unique solution to 3 x 5 (mod 11) by Theorem 20.1.7. #21.3 Below is the multiplication table mod 12. We see that 5 is invertible and is its own inverse. Similarly, 7 is invertible and is its own inverse. Finally 11 is invertible and is its own inverse. X 1 2 3 4 5 6 7 8 9 10 11 1 1 2 3 4 5 6 7 8 9 10 11 2 2 4 6 8 10 2 4 6 8 10 3 3 6 9 3 6 9 3 6 9 4 4 8 4 8 4 8 4 8 5 5 10 3 8 1 6 11 4 9 2 7 6 6 6 6 6 6 6 7 7 2 9 4 11 6 1 8 3 10 5 8 8 4 8 4 8 4 8 4 9 9 6 3 9 6 3 9 6 3 10 10 8 6 4 2 10 8 6 4 2 11 11 10 9 8 7 6 5 4 3 2 1 #23.2 Solution: We have 4148 = 2 2 17 61 and 7684 = 2 2 17 113. Hence gcd(4148,7684) = 2 2 * 17 = 68....
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 Spring '06
 Knutson
 Math

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