query: Find all natural numbers n such that $\phi(n)$=12
positive_passages.docid: 124220
positive_passages.text: Using Euler's Totient Function, how do I find all values n such that $\phi(n)=12$?
negative_passages.docid: 78342
negative_passages.text: When is $\phi(n)$ a prime number?
negative_passages.docid: 114136
negative_passages.text: Euler's $\phi(n)$ function and solutions of $\phi(n) = 4294967296=2^{32}$
negative_passages.docid: 8771
negative_passages.text: Finding the nth non square free number
negative_passages.docid: 46065
negative_passages.text: How do you find all $n$ such that $\phi(n)|n$
negative_passages.docid: 9753
negative_passages.text: How to solve the equation $\phi(n) = k$?
negative_passages.docid: 48655
negative_passages.text: Find all n such that : $3 \mid (n2^{n}+1)$
negative_passages.docid: 52951
negative_passages.text: Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
negative_passages.docid: 46741
negative_passages.text: Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
negative_passages.docid: 77171
negative_passages.text: How to find unique multisets of n naturals of a given domain and their numbers?
negative_passages.docid: 8884
negative_passages.text: Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
negative_passages.docid: 146665
negative_passages.text: Prove that $f(x)=8$ for all natural numbers $x\ge{8}$
negative_passages.docid: 136623
negative_passages.text: Hints/ Solution in finding a formula $\phi(n)$ for a binary square matrix
negative_passages.docid: 130542
negative_passages.text: Every natural number $n$ can be written as $n=s-t$ with $\omega(s)=\omega(t)$
negative_passages.docid: 115258
negative_passages.text: Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.
negative_passages.docid: 44577
negative_passages.text: Finding a formula to sum natural numbers up to $n$
negative_passages.docid: 109440
negative_passages.text: How does $(12\dots n)$ and $(a\, b)$ generate $S_n$?