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.

If $\phi(n)$ is the Euler-totient function, how can I show that $\phi(n) \ge \sqrt{n}$?

share|improve this question
4  
$\varphi(2)=1<\sqrt2$. –  Brian M. Scott Feb 20 '13 at 2:00
    
I'm sure this question has been asked, and answered, here, but I'm not sure how to find it. –  Gerry Myerson Feb 20 '13 at 2:01
2  
$\varphi(6) = 2 < \sqrt{6}$ –  mixedmath Feb 20 '13 at 2:01
1  
See, for example, math.stackexchange.com/questions/301837/… --- especially Brian's answer. –  Gerry Myerson Feb 20 '13 at 2:08
    
@Gerry, math.stackexchange.com/questions/301837/… –  Will Jagy Feb 20 '13 at 2:08
show 2 more comments

1 Answer

Hint: both $\phi(n)$ and $\sqrt{n}$ are multiplicative, so it suffices to consider prime powers.

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.