prove that the order of $2$ mod p is $2^{n+1}$
100361
Show that ord$_{p}2 = 2^{n + 1}$.
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
23830
Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
102234
Show $a^p \equiv a \mod 2p$
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
94855
Prove if a (mod n) has a multiplicative inverse, then it's unique