query: Compute $\phi^{-1}(k)$, $\phi$ Euler's totient function?
positive_passages.docid: 9753
positive_passages.text: How to solve the equation $\phi(n) = k$?
negative_passages.docid: 82448
negative_passages.text: Why is $f(x) = x\phi(x)$ one-to-one?
negative_passages.docid: 117681
negative_passages.text: For which Natural $n\ge2: \phi(n)=n/2$
negative_passages.docid: 142931
negative_passages.text: Problem on Euler's Phi function
negative_passages.docid: 146762
negative_passages.text: Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
negative_passages.docid: 102942
negative_passages.text: Compute the sum $\sum_{k=1}^{\infty}k^mz^k$ where $|z|<1$
negative_passages.docid: 104982
negative_passages.text: Determine $\phi(2^{399}+1)$
negative_passages.docid: 57416
negative_passages.text: Fibonacci identity: $f_{n-1}f_{n+1} - f_{n}^2 = (-1)^n$
negative_passages.docid: 8784
negative_passages.text: modulo version of the quadratic formula and Euler's criterion
negative_passages.docid: 121723
negative_passages.text: $\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k
negative_passages.docid: 35525
negative_passages.text: Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula
negative_passages.docid: 123036
negative_passages.text: Is the equation $x = \phi(n), x=2k, n,k \in \mathbb{Z}$, where $\phi(n)$ is the Euler totient function, solvable for all evens?
negative_passages.docid: 4512
negative_passages.text: Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
negative_passages.docid: 82878
negative_passages.text: Order of cyclic groups and the Euler phi function
negative_passages.docid: 136623
negative_passages.text: Hints/ Solution in finding a formula $\phi(n)$ for a binary square matrix
negative_passages.docid: 154001
negative_passages.text: $(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
negative_passages.docid: 149589
negative_passages.text: Analogous results to Euler's theorem