Prove that 18 | a if and only if 2 | a and 9 | a
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
132971
Prove that $|a| < b \iff -b<a<b$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
60122
Prove $(1+a+b)(1+b+c)(1+c+a)\ge 9(ab+bc+ca)$
105768
Proof involving absolute value and maximums
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
133699
Proving that there is a bijection between $A$ and $B$.
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
32929
Questions about proving $\lnot \lnot a = a$
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
81618
Prove $||a|-|b| | \leq |a-b|$