MATH 311W Quiz: Math 311w quiz03

• School: PSU
• Department: Mathematics
• Course: MATH 311W
• Professor: All

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Instructions: clearly answer each of the questions below. Remember to check the back side if blank, you can use it for scrap work. Show your work and any formulas you employ. Answer:a congruence class [a]n is the set of all integers having the same remainder as a after division by n: find [9] 1. 49 using the matrix gcd method, if it exists. 9 (cid:21) (cid:20) 1 0 49 (cid:20) 0. So 2(49) + 11(9) = 1, or in congruence classes, [ 2(49) + 11(9)]49 = [11]49[9]49 = [1]49, which means. 26 using the matrix gcd method, if it exists. Answer:does not exist, since gcd(6, 26) = 2 > 1: find [5]9[7]9 + [3]9. Let"s prove that if [a]n is invertible, then [a]n is not a zero-divisor. Suppose that there is some congruence class [z]n such that [a]n[z]n = [0]n. (a) there is a congruence class [i]n such that [i]n[a]n = [1]n, because