Prove $n \choose m$ is divisible by n when $\gcd(m,n)=1$
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
106847
Proof that $n^3+2n$ is divisible by $3$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
52032
Prove that ${n^5 - n}$ is divisible by 5
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$