Prove that $(a,bc)=1$ if and only if $(a,b)=1$ and $(a,c)=1$
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
127296
prove that a|b and b|a iff a=+-b
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
100571
Prove $(1-a)(1-b)(1-c)(1-d)\geq abcd$ if $a^2+b^2+c^2+d^2=1$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
33240
$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $, prove $ab + bc + ca \le 3$
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$