Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I know that a group of order 5 does not have any nontrivial factors and that you cannot factor 5 as a product of two numbers larger than 1 but I do not know where to go from here?

share|improve this question
add comment

3 Answers 3

HINT: If $a$ is an element of order $5$, what is the order of $a^2$?

share|improve this answer
add comment

Hint: Prove that for any g, $o(g) = o(g^{-1})$.

The statement will remain true when 5 is replaced by any $n \geq 3$.

share|improve this answer
    
Sorry, I was confused. –  Graphth Sep 26 '12 at 23:57
add comment

If $x$ has order $5$, it means, $x^5=1$ in the group. So, $x^2$ will also have order 5, but $x^2\ne x$ because then $x=1$ would follow by division.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.