If $m = a_1x+b_1y$ , $n = a_2x+b_2y$ and $a_1b_2-a_2b_1 = 1$ then prove that $(m,n) = (x,y)$ arithmetic divisibility
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
118918
Understanding a proof that $2x + 3y$ is divisible by $17$ iff $9x + 5y$ is divisible by $17$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
145889
Prove if $56x = 65y$ then $x + y$ is divisible by $11$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
29692
Proof verification: elementary Number Theory Proof of $am+bn = 1$