Show for all primes $p>11$ there are two consecutive quadratic residues
17786
Existence of Consecutive Quadratic residues
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
84746
elementary proof that infinite primes quadratic residue modulo $p$
71788
Prove existence of multiplicative inverse modulo p when p is prime
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.
40156
Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$
26503
Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
157131
Show that all Fermat numbers pass the base $2$ test (pseudoprime).
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
46820
If $p$ is a prime such that $p≡1\pmod 7$ then $p ≡1\pmod{14}$
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
93898
Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
37330
Prove that any two consecutive terms of the Fibonacci sequence are relatively prime
144575
Factoring n, where n=pq and p and q are consecutive primes
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.