Sum of squares of the quadratic nonresidues modulo $p$ is divisible by $p$
128584
Sum of squared quadratic non-residues
27287
$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
50128
Efficiently finding two squares which sum to a prime
80671
Product of sums of square is a sum of squares.
55621
Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
49234
Sum of binomial coefficients with index divisible by 4
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
94060
Sum of square binomial coefficients
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
75318
How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?
58264
How to derive the formula for the sum of the first $n$ perfect squares?
127816
Number theory proof mod p
25910
Product of Quadratic Residues