If a is an element of order m in a group G and a^(k) = e, prove that m divides k.
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Do a long division on the exponent.
Originally Posted by FancyMouse Do a long division on the exponent. I don't understand what you mean. Can you explain?
Originally Posted by rainyice I don't understand what you mean. Can you explain? Let k=rm+q where r is an integer and 0<=q<m. What can you say about ?
Originally Posted by FancyMouse Let k=rm+q where r is an integer and 0<=q<m. What can you say about ? it has infinite order?
, where . So, Since , what is the only such that gives ?
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