The equation $\phi (x)=n$ has only a finite number of solutions.
71108
Is there an integer $N>0$ such that $\varphi(n) = N$ has infinitely many solutions?
33314
How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
117352
Show $x^n+ax+b=0$ has most two solutions
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
114906
For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
77990
How many solutions $X^{10} - I=0$ has in $M_2(\mathbb{R})$?
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
27540
A polynomial can not have infinite number of constant values
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
51445
Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$
121723
$\phi(n)=\frac{n}{2}$ if and only if $n=2^k$ for some positive integer k
158582
Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
113695
Show that there is no integer n with $\phi(n)$ = 14