Prove: If $a$ divides $b c$ and $1 = a r + c s$, then $a$ divides $b$, where $a,b,c,r$ are integers.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
6970
If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
67528
"If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer"
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
58579
Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$