For any odd prime $p≥5$, $(-3/p) = 1$ if $p ≡ 1,-5\pmod{12}$ and $(-3/p) = -1$ if $p ≡ -1,5 \pmod{12}$
29979
When is $-3$ a quadratic residue mod $p$?
121441
$1\cdot3\cdot5 \cdots (p - 2) = (-1)^{m+k+1} \pmod p$, and $2\cdot4\cdot6\cdots(p - 1) = ( -1)^{m +k} \pmod p$.
140948
Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.
79208
Is the number $-1$ prime?
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
71788
Prove existence of multiplicative inverse modulo p when p is prime
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
15436
Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
27287
$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
85272
$3x + 1$ is even iff $5x-2$ is odd
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
76807
How come if $\ i\ $ not of the following form, then $12i + 5$ must be prime?
48875
$n^3 \equiv n^5 \pmod{12} $?