4023f11ps2

# 4023f11ps2 - G and H . The easiest way to verify that G...

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Homework #2 Due: September 7, 2011 1. Find d = gcd( m; n ) and write d in the form d = sm + nt for each of the following pairs of integers m and n . (a) m = 56, n = 72. (b) m = 119, n = 272. (c) m = 513, n = 187. (d) m = 1769, n = 2378. 2. For each of the following elements of Z 81 , ﬂnd the multiplicative inverse, or explain why there is not a multiplicative inverse. (a) a = 21 (b) b = 25 3. Determine if each of the following subsets of Z 10 is a group using the binary operation of + modulo 10. You may assume that the associative law holds in Z 10 , and hence you do not need to verify it for
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Unformatted text preview: G and H . The easiest way to verify that G and/or H are groups may to be form a Cayley table. See Page 15. (a) G = f ; 2 ; 4 ; 6 ; 8 g (b) H = f ; 3 ; 6 ; 9 g 4. Determine if each of the following subsets of Z / 13 is a group using the binary operation of multiplication modulo 13. You may assume that the associative law holds in Z / 13 , and hence you do not need to verify it for G and H . (a) G = f 1 ; 3 ; 6 ; 9 ; 12 g (b) H = f 1 ; 5 ; 8 ; 12 g Math 4023 1...
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## This document was uploaded on 12/28/2011.

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