Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
9997
For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
127293
Prove that $(a-b) \mid (a^n-b^n)$
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
126574
Proving $\prod_k \sin \pi k / n = n / 2^{n-1}$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
39217
If $d \mid n$ then $x^{q^d} - x \mid x^{q^n} - x$.
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$