# Thread: phi(n)=2^31

1. ## phi(n)=2^31

Find an odd number n with phi(n)=2^31.

Thank you very much.

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

Thank you very much.
$n=2^{31}+1$
This is a Mersenne Prime.
And its phi function is 1 less.

3. I got a different question for you.
Find a number such that,
$\phi(n)=31^2$

4. 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.

5. 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,
$\phi(n)$ is always even for $n>1$.