Let $a,b,c$ be positive real numbers such that $abc =1$
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
154822
Properties of the composition law $a @ b= ab + b + a$ on the real numbers
89792
Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
19909
if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
98002
Let $x$ be a positive real number. Inequality problem with $\pi$ and $x$ terms.
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
149287
Prove that $A,B>0$ and $A_{ij}0$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
77212
Show that for any real constants a and b, where b > 0, (n + a) b = Θ(n b ).
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$