Let , , and suppose is the order of a mod r, and is the order of a mod s. Let . Show that is the order of a mod m. So we know: Now, what?
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Your notation is terribly confusing. You're saying that is the order of mod , and is the order of mod , and thus that is the order of mod ? Hint: use the Chinese remainder theorem. There is an isomorphism .
Originally Posted by Bruno J. Your notation is terribly confusing. You're saying that is the order of mod , and is the order of mod , and thus that is the order of mod ? Hint: use the Chinese remainder theorem. There is an isomorphism . I am not sure what do by using the CRT but here is what we have: So I don't know how I am supposed to proceed.
Do you know a bit of algebra? What is the order of an element in the direct product of two finite groups?
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