number theory : let $a \in \mathbb Z^+$ find $(a,a+1)$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
6837
How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$?
131971
If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
137186
Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
39492
Finding $z\in \mathbb C$ with $\sin z = 2$?
16382
Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
110695
Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
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 $a$.
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
81267
A simple doubt in number theory problem.
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$