If $a|N$ and $b|N$ where $a,b$ are coprime , is it necessary that $(a \times b) |N$?
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
156910
Necessary and sufficient condition for $R/IJ \cong R/I \times R/J$
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
62566
Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?
138669
proving that elements of a sequence are pairwise coprime
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
116361
Relationship between prime factorizations of $n$ and $n+1$?
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
100549
If $e^A$ and $e^B$ commute, do $A$ and $B$ commute?