Show that $\bf (a^\top Q b)^2 \le a^\top Q a \ b^\top Q b$!
33673
Proving $N(x) = (A(x,x))^\frac12$ is a norm in $V$ given that A is a positive definite bilinear form
80009
Prove that $| |a|-|b| | \le |a-b|$
108237
Show $a^p \equiv b^p \mod p^2$
152817
Proving $\sup B=\inf A$
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
69921
Prove that: $(1+a_1)(1+a_2)...(1+a_n) \le 1 + S_n + (S_n)^2/2! + ... + (S_n)^n/n!$
15104
Show that $\big|\frac{a-b}{1-\overline{a}b}\big|=1$, when either $|a|=1$ or $|b|=1$.
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
50142
If sup A $\lt$ sup B show that an element of $B$ is an upper bound of $A$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
87813
How to show that for all k, $k! \ge (k/2)^{k/2}$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$