4383_HW05_Sp112 - ( 29 53 19 mod503 . Show your work! 5....

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Math 4383 Spring 2012 Homework 5 Sections 4.2, 4.3, 4.4 The notation [ ] n x denotes the congruence class of the integer x modulo n. The set n is the set of all distinct congruence classes (residue classes) modulo n. See the “extra 4.2 notes” for definitions. 1. Perform the indicated arithmetic in 12 . a. 12 12 [10] [11] + = b. 12 12 [5] *[11] = c. ( 29 3 12 [41] d. 12 12 [3] *[15] 2. Construct the multiplication table for 9 3. For each invertible element [x] in 9 , find its powers, ( 29 9 [ ] k x , for k = 1,2,3,4,5,6,7,8,9. 4. Use the binary representation of the power to find
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Unformatted text preview: ( 29 53 19 mod503 . Show your work! 5. For any integer a, show that 2 7- + a a ends in one of the digits 3, 7 or 9. 6. Find the remainder when 4444 4444 is divided by 9. Show your work! 7. Section 4.4 Exercise # 11 8. Section 4.4 Exercise # 12 9. Find an integer x < 1200 which leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, a remainder of 5 when divided by 7, and a remainder of 1 when divided by 11....
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This note was uploaded on 02/21/2012 for the course MATH 4383 taught by Professor Flagg during the Spring '09 term at University of Houston.

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