Show for any odd prime $p\geq 5,$ $(-3/p)=1$ or $ -1$
29979
When is $-3$ a quadratic residue mod $p$?
51520
Prove that the only prime triple is 3, 5, 7
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
71788
Prove existence of multiplicative inverse modulo p when p is prime
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
110809
What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$?
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
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 $x-1$
131241
primes congruent to 5 mod 6 and 1 mod p
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
68824
Show that $\frac{(3^{77}-1)}{2}$ is odd and composite
126494
Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.