If $a\equiv b\pmod m$ and $c+d\equiv 0\pmod m$ then $ac+bd\equiv 0\pmod m$
141369
If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
55680
The relationship of ${\frak m+m=m}$ to AC
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
978
Solving $ax \equiv c \pmod b$ efficiently when $a,b$ are not coprime
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
91285
Prove $a+b+c+d $ is composite
13026
Prove that if AB=I_m, then rk(A)=rk(B).
32463
$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
18119
Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
70006
$a,b,m,n$ be positive integers such that g.c.d.$(a,b)=1$ and $a^m+b^m|a^n+b^n$ , then $m|n$?
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$