A and B are groups with binary operationsand ?
Prove that the order ofis
The binary operation ofis define as such:
Letand
.
Do I need to define the gcd as well? Regardless if I do or not, I am not sure where to proceed next.
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A and B are groups with binary operations
Prove that the order of
The binary operation of
Let
Do I need to define the gcd as well? Regardless if I do or not, I am not sure where to proceed next.
LCM(n, m) is the smallest integer that is both a multiple of both n and m. By definition the order ofwith
. By definition of the order of a and b, we know that
and
. Therefore, k is the least such integer such that k =
and k =
(these expressions come from definition of n "divides" k, or "n | k"). This means, overall, that k is the least such integer that is a multiple of both n and m.