Proof verification - If $a|bc$ and $(a,b) = 1$, then $a|c$
21241
Proving $\,a\mid bc\!\iff\! \frac{a}{(a,b)}\!\mid c\ $ [general Euclid's Lemma]
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
23694
Given that $abc=1$, prove that $\frac{b}{c} + \frac{c}{a}+ \frac{a}{b} \ge \frac{1}{a} + \frac{1}{b} +\frac{1}{c}$.
6970
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
13026
Prove that if AB=I_m, then rk(A)=rk(B).
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
13136
Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
31783
Is this proof of $ab = 0$ correct?
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]