Prove that $a/b+b/c+c/a \geq a+b+c$ if $abc=1$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
41792
If $abc=1$, then $\frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
60122
Prove $(1+a+b)(1+b+c)(1+c+a)\ge 9(ab+bc+ca)$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
92300
For positive $a$, $b$, $c$ with $abc=1$, show that $\sum_{cyc}\sqrt{a^2-a+1}\geq a+b+c$
89175
Proof of $(a+b)^{n+1}$
90670
Prove $a^ab^bc^c\ge (abc)^{\frac{a+b+c}3}$ for positive numbers.
15116
Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
17264
Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$