Why does this result only apply to primes congruent 3 mod 4?
140198
Let $a$ be a quadratic residue modulo $p$. Prove that the number $b\equiv a^\frac{p+1}{4} \mod p$ has the property that $b^2\equiv a \mod p$.
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
30725
Why are naturals < modulus equal if congruent? [uniqueness of remainder]
113359
Proving that $x^2 + 4$ is not divisible by $3$
73020
Every integer is congruent to the sum of its digits mod 9
36182
Why doesn't the last digit method work for divisibility by 4?
95653
Euler's theorem: [3]^2014^2014 mod 98
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
77969
Question about proof for $S_4 \cong V_4 \rtimes S_3$
110809
What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$?
157766
Are primes (ignoring $2$) equally likely to be $1~\text{or}~3\pmod 4$?
106313
How Does Modulus Divison Work
131395
Solving linear congruence $2x + 11 \equiv 7 \pmod 3$
52530
There exists a prime congruent to $m$ mod $p$
151636
Fast way to calculate n! mod m where m is prime?
9787
Primitive roots modulo primes congruent to n!
57654
Congruent Modulo $n$: definition