Prove That $6^n -1$ is composite
2522
Why is $a^n - b^n$ divisible by $a-b$?
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
80144
Prove that $x-1$ divides $x^n-1$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
80242
Prove that $n^{2003}+n+1$ is composite for every $n\in \mathbb{N} \backslash\{1\}$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
75329
Use induction to prove that $F_n \ge \sqrt 2 ^n$ for $n \ge 6$
77383
Prove that $n^3=n \text{ mod }6$ for every integer $n$.
71880
Prove that every prime factor of $12x^2+1$ has the form $6n+1$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
46102
Prove that $2^n +1$ in never a perfect cube
134963
Proving a non-prime (composite) number $> 1$ has a divisor $d \leq\sqrt q$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$