Let $q$ be a prime integer. Show that for each $x∈GF(q)$ there exist elements $r$ and $s$ in $GF(q)$ satisfying $x=r^2+s^2$.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
22248
$G$ solvable $\implies$ composition factors of $G$ are of prime order.
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
91180
Show $R \setminus S$ is a union of prime ideals
4402
Group of order $pqr$, $p < q < r$ primes
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
50412
Prime elements in $\mathbb{Z}/n\mathbb{Z}$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
98474
Show the existence of a certain subgroup of F2
119657
If $ f _p(x)=1+x+x^2+ \cdots +x^{p-1} $ where $p$ is prime number, $e$ is any positive integer.
19016
Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
72666
Prime Numbers And Perfect Squares
125330
How to find element g order q, given 2 large primes p and q where q|p-1
99630
For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?