If for a prime $q$ holds $q \equiv 5 \pmod 8$, then $q-2$ has a prime factor $p$ with $p \equiv 3 \pmod 8$ or $p \equiv 5 \pmod 8$
106111
Understanding that there are infinitely many primes of form $4n+3$
92737
primes whose difference is a multiple of $n$
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
102204
Factoring product of two primes from solutions of congruence
19016
Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
85287
Prove that, for $p > 3$, $(\frac 3p) = 1$ when $p \equiv 1,11 \pmod{12}$ and $(\frac 3p) = -1$ when $p \equiv 5,7 \pmod{12}$
121717
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.
87282
Diophantine equation involving prime numbers : $p^3 - q^5 = (p+q)^2$
110809
What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$?
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
31312
If a prime divides a product then it must divide a factor of the product [Euclid's Lemma]
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$