The positive zero of the equation $x^n+x^{n-1}+x-1=0$
42251
Limit of non-negative real root of $x^n+x^{n-1}+x-1=0$ as $n \to \infty$
5287
Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$
8360
$\sum_i x_i^n = 0$ for all $n$ implies $x_i = 0$
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
131876
Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
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.
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
55266
Prove that $(n+1)^{n-1}<n^n$
33989
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
53866
Prove $ x^n-1=(x-1)(x^{n-1}+x^{n-2}+...+x+1)$
41411
How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$
28502
How to solve $x^3=-1$?
158335
Why is this $0 = 1$ proof wrong?
136077
Prove that $x-1$ is a factor of $x^n-1$
2408
Show that a polynomial has at least one positive solution/root.