Prove $|xax^{-1}| = |a|$
83452
Prove that any conjugate of $a$ has the same order as $a$.
80144
Prove that $x-1$ divides $x^n-1$
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
49438
Prove that $X^\ast$ separable implies $X$ separable
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
14161
Proof of when is $A=X^TX$ invertible?
15232
Proving an inequality involving real powers
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
136077
Prove that $x-1$ is a factor of $x^n-1$
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
89637
Proof that in a field $x=0$ is equivalent to $x=-x$
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
80009
Prove that $| |a|-|b| | \le |a-b|$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.