Proof that $a^b>b^a$ if $a<b$ are integers larger or equal to two and $(a,b)\neq (2,3),(2,4)$
26062
Given $a>b>2$ both positive integers, which of $a^b$ and $b^a$ is larger?
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
10604
Prove $3^n > n^2$ by induction
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
113168
If $a > b$, is $a^2 > b^2$?
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
6621
Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$
130093
Prove by Induction : $n < 2^n$
81618
Prove $||a|-|b| | \leq |a-b|$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, 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 $ad=bc$.