# Math Help - True or false

1. ## True or false

Is this statement true or false: "If $\phi$ denotes the Euler-Phi function, there is a unique value of the number n for which $\phi(n)=12$".

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$\phi(13)=12$. How can I prove (or disprove) that there isn't another?

2. Well, $12=(3-1)(7-1)$ so $\varphi(21)=12.$

3. What did you do there?

Also, looking on wiki, there's another: $\phi(28)=12$

4. Originally Posted by Showcase_22

What did you do there?
We know that if p and q are prime numbers, then $\varphi(pq)=(p-1)(q-1)$

Then, playing with the factors of 12 will bring you to the solution he found.

5. $\phi(13)=13-1=12$