Further concepts and computations. 7) Much like we defined addition modulo n in Zn, we can also define multiplication modulo n. For example in Z5, 4+n 3=(4+3)mod5=7mod5=2,wecanalsodefine multiplication modulo n. For example in Z5,3 .5 4=3×4mod5=12mod5=2because 3 × 4 = 12 = 2(5) + 2. Show that the subset {1, 3, 5, 7} of Z8 with multiplication modulo 8, .8 is a group, and give the table for this group.
Further concepts and computations. 7) Much like we defined addition modulo n in Zn, we can also define multiplication modulo n. For example in Z5, 4+n 3=(4+3)mod5=7mod5=2,wecanalsodefine multiplication modulo n. For example in Z5,3 .5 4=3×4mod5=12mod5=2because 3 × 4 = 12 = 2(5) + 2. Show that the subset {1, 3, 5, 7} of Z8 with multiplication modulo 8, .8 is a group, and give the table for this group.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Further concepts and computations.
7) Much like we defined addition modulo n in Zn, we can also define multiplication modulo n. For example in Z5,
4+n 3=(4+3)mod5=7mod5=2,wecanalsodefine multiplication modulo n. For example in
Z5,3 .5 4=3×4mod5=12mod5=2because
3 × 4 = 12 = 2(5) + 2.
Show that the subset {1, 3, 5, 7} of Z8 with multiplication modulo 8, .8 is a group, and give the table for this group.
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