For $c \in \mathbb{R}$, the equation $\dfrac{1}{x-a_1} + \dfrac{1}{x-a_2} + \ldots + \dfrac{1}{x-a_n} = c$ has $n-1$ real solutions
59065
Roots to an equation using analysis
79925
Infinitely many values of $x$ that satisfy the equations
76716
Solve an equation in $\mathbb{R}^+$
56928
$\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}\in\Bbb Z\,\Rightarrow\, \dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}\in\Bbb Z$
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
126820
How many positive integer solutions are there to the equality $x_1+x_2+...+x_r= n$?
156542
Number of solutions to $a_1 + a_2 + \dots + a_k = n$ where $n \gt 0$ and $0 \lt a_1 \leq a_2 \leq \dots \leq a_k$ are integers.
23485
Solving $\forall x \in \mathbb{R}_+^*, f'(x) = f\left(\frac1{x}\right)$
103993
Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
68771
Assume that $ 1a_1+2a_2+\cdots+na_n=1$, where the $a_j$ are real numbers.
20834
Integer solutions to $c=a^2-b^2$
134736
Prove using Rolle's Theorem that an equation has exactly one real solution.
104319
Real solution of $(\cos x -\sin x)\cdot \bigg(2\tan x+\frac{1}{\cos x}\bigg)+2=0.$
42713
Solutions to the equation $ze^{a-z}=1$
18702
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
107765
Prove that there exists two roots in $[-1,1]$
118368
number of real solution of logarithmic and exponential equation