How can I prove $q+1 \vert q^n + 1 \iff \ n$ is odd
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
65466
How to prove this Fibonacci sequence statement: $F^2_{n+1} - F^2_{n-1} = F_{2n}$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
18953
Prove that even + odd is odd.
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
55582
How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$