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2.3 Since m is not a prime, it can be factored as the product of two integers a and b,
m = a ¢ b
with 1 < a; b < m. It is clear that both a and b are in the set f1; 2; ¢ ¢ ¢ ;m ¡ 1g. It follows
from the definition of modulo-m multiplication that
a ¡ b = 0:
Since 0 is not an element in the set f1; 2; ¢ ¢ ¢ ;m¡1g, the set is not closed under the modulo-m
multiplication and hence can not be a group.
Lin Shu , error control coding , 2nd edition
林舒《error control coding》第2版原版的部分答案,希望对大家有点用
[ 本帖最后由 doocao 于 2008-10-4 13:37 编辑 ] |
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