2007 iTest Problems/Problem 14

Problem

Let $\phi(n)$ be the number of positive integers $k< n$ which are relatively prime to $n$ . For how many distinct values of $n$ is $\phi(n)=12$ ?

$\text{(A) } 0 \quad \text{(B) } 1 \quad \text{(C) } 2 \quad \text{(D) } 3 \quad \text{(E) } 4 \quad \text{(F) } 5 \quad \text{(G) } 6 \quad \text{(H) } 7 \quad \text{(I) } 8 \quad \text{(J) } 9 \quad \text{(K) } 10 \quad \text{(L) } 11 \quad \text{(M) } 12\quad \text{(N) } 13\quad$

Solution

See https://artofproblemsolving.com/community/q2h598845p3554139.

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2007 iTest Problems/Problem 14

Problem

Solution