Proof: For any prime number $p$, there must be integer $a$, $b$, $c$, $d$ such that $x^4+1 \equiv (x^2+ax+b)(x^2+cx+d)\ (mod\ p)$.
16592
Irreducible polynomial which is reducible modulo every prime
130300
Proof that every quadratic residue has two roots, modulo a prime
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
102046
If all primes greater than some fixed value are congruent one modulo an integer, then said integer is equal two.
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
93898
Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.