Prove that $(a + 2b + 3c + 4d)a^a b^b c^c d^d < 1 $.
6280
Homogenization, what it is in inequalities and how to utilize it to its fullest.
6621
Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
89175
Proof of $(a+b)^{n+1}$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
94383
Prove that $A^TD-C^TB=I$
136868
Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
100571
Prove $(1-a)(1-b)(1-c)(1-d)\geq abcd$ if $a^2+b^2+c^2+d^2=1$
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
18606
How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
150289
A number with an interesting property. $abcd=a^b c^d$
37536
Inequality: $ab^2+bc^2+ca^2 \le 4$, when $a+b+c=3$.
109133
$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$
107173
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$