Is exactly one of $a, a + b^n, ..., a + b^{p - 1}$ divisible by $p$?
130162
A complete residue system from an arithmetic progression
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
150528
Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
89175
Proof of $(a+b)^{n+1}$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
12694
Why does $a^n - b^n$ never divide $a^n + b^n$?
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
46431
Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$