let $ a,b \in (0,1)$ ,$a+b>1$ then : prove that : $2^a+3^b<3a+4b$
111267
Prove that: $2^a+3^b<3a+4b$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
56315
Prove $\frac{|a+b|}{1+|a+b|}<\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$.
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
55266
Prove that $(n+1)^{n-1}<n^n$
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
129480
Prove that inf(A+B) = infA + infB
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
152817
Proving $\sup B=\inf A$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$