# phi(n)=2^31

• Jan 2nd 2007, 10:41 AM
Jenny20
phi(n)=2^31
Find an odd number n with phi(n)=2^31.

Thank you very much.
• Jan 2nd 2007, 10:47 AM
ThePerfectHacker
Quote:

Originally Posted by Jenny20
Find an odd number n with phi(n)=2^31.

Thank you very much.

$\displaystyle n=2^{31}+1$
This is a Mersenne Prime.
And its phi function is 1 less.
• Jan 2nd 2007, 10:56 AM
ThePerfectHacker
I got a different question for you.
Find a number such that,
$\displaystyle \phi(n)=31^2$
• Jan 2nd 2007, 11:42 AM
Jenny20
hi perfecthacker,

Please do teach me. I do not know how to get it backward for the n.

If you ask me what is phi(6912) , then I can easily tell you that is 2304. But if you give me an answer and ask me to get back to n, i have no idea how to get it. :(
• Jan 2nd 2007, 01:28 PM
ThePerfectHacker
Quote:

Originally Posted by Jenny20
hi perfecthacker,

Please do teach me. I do not know how to get it backward for the n.

If you ask me what is phi(6912) , then I can easily tell you that is 2304. But if you give me an answer and ask me to get back to n, i have no idea how to get it. :(

My question was a trick question. Because,
$\displaystyle \phi(n)$ is always even for $\displaystyle n>1$.