Prove that there exist integers $a$ and $b$, so $am + bn = 1$.
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
133699
Proving that there is a bijection between $A$ and $B$.
46286
Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.
6096
If $A+B=AB$ then $AB=BA$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
143130
Proving that the supremum of $(a,b)$ is $b$.
24856
Proving sup(A + B) = sup A + sup B
59535
Prove that there exists such a set of $n$ positive integers
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
149287
Prove that $A,B>0$ and $A_{ij}0$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$