4023f10ps3

4023f10ps3 - 2565 in Z 2565(b[423 6087 in Z 6087 5 Solve...

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Homework #3 Due: September 20, 2010 1. Determine if each of the following statements is true or false. (a) 40 · 13 mod 9 (b) ¡ 29 · 1 mod 7 (c) ¡ 29 · 6 mod 7 (d) 132 · 0 mod 11 2. Find all the solutions (when there are any) of the following linear congruences: (a) 8 x · 6 mod 14 (b) 66 x · 100 mod 121 (c) 21 x · 14 mod 91 (d) 21 x · 14 mod 89 3. Find the inverse of 13 modulo 35 and use it to solve the equation [13] 35 x = [9] 35 in Z 35 . 4. Find the multiplicative inverses of the given elements (if possible). (a) [91]
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Unformatted text preview: 2565 in Z 2565 (b) [423] 6087 in Z 6087 5. Solve the following systems of linear congruences: (a) x · 4 (mod 24) x · 7 (mod 11) (b) x · 3 (mod 5) x · 4 (mod 7) x · 3 (mod 8) 6. In Z 18 flnd all units and all zero divisors. 7. Find (a) 6 76 mod 13, (b) 7 1001 mod 11, (c) 2 25 mod 21, (d) 7 66 mod 120. 8. Calculate ’ (32), ’ (33), ’ (120), and ’ (384). ( ’ ( n ) is the Euler ` function evaluated at n .) Math 4023 1...
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This document was uploaded on 12/28/2011.

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