Show that if , where and for every , then is a Carmichael number.
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Originally Posted by chiph588@ Show that if , where and for every , then is a Carmichael number. We will show that if and then . Define the group . Now then is the identity because and . Therefore, if then we see that is the identity. Thus, .
Is there a way to do it without fields?
Originally Posted by chiph588@ Show that if , where and for every , then is a Carmichael number. suppose then for all let by Fermat's little theorem: for all thus so, since are distinct, we'll have
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