Suppose $a$, $b$, and $c$ are integers. Prove that if $a \mid b$ and $a \mid c$, then $a \mid (b +c)$
13466
Prove that if a|b and b|c then a|c using a column proof that has steps in the first column and the reason for the step in the second column.
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
35242
If $a$, $b$, $c$, $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$, and $\frac{a}{c}+\frac{b}{a}+\frac{c}{b}$ are all integers, then $|a|=|b|=|c|$
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
39779
If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$