Prove that $\sum a_i e^{\alpha_ix}=0$ has at most $n-1$ real solutions.
73478
Show that the equation $a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$ has at most $n - 1$ real roots.
77990
How many solutions $X^{10} - I=0$ has in $M_2(\mathbb{R})$?
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
15232
Proving an inequality involving real powers
24837
$x^2+1=0$ uncountable many solutions
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
51153
Number of solutions to $x^2\equiv a\pmod m$
69288
Number of real roots of $\sum_{k=0}^{n}\frac{x^{k}}{k!}=0$
134736
Prove using Rolle's Theorem that an equation has exactly one real solution.
117352
Show $x^n+ax+b=0$ has most two solutions
103832
Number of solutions of $x_1 + x_2 + x_3 + x_4 = 14$ such that $x_i \le 6$
102391
Abel summability under the hypothesis $a_n \ge 0$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
127169
Show that the zeros of $\sum_{k=1}^n kz^{k-1}$ are inside the unit disc
38090
Partial sums of $nx^n$
54703
Find the a < 0 for which the inequalities have at least one common solutions