What are the conditions for a and b if given a | b^2, it follows that a | b?
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
121759
If this equation in x has real roots find the value of a and b.
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
80789
Prove that $\forall a,b,c,d\in \mathbb{R}\,$, $(a^2-b^2)(c^2-d^2)\leq(ac-bd)^2$ and equalities hold if and only if $ad=bc$.
101519
What is the condition for example $(number^c)^b=number^{cb}$ to be true?
81618
Prove $||a|-|b| | \leq |a-b|$
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
5729
If $a^2+b^2+c^2=1$ then prove the following.
62172
Why does $-b < a < b \iff |a| < b$?
96630
Let a and b be real numbers such that 0  \sqrt{ab} > \frac{2ab}{a + b}$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $