Let $a$ and $b$ be positive integers. Prove that $(a,b)|[a,b]$.
48452
Proof that $\gcd$ divides $\operatorname{lcm}$
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
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 $a=b$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
26062
Given $a>b>2$ both positive integers, which of $a^b$ and $b^a$ is larger?
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
133699
Proving that there is a bijection between $A$ and $B$.
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
101362
Let a,b,c be positive real number, proof.
143130
Proving that the supremum of $(a,b)$ is $b$.
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?