the only solution of prime $q|(p^2-1)$ with $p<q$ is $p=2$ and $q=3$.
31312
If a prime divides a product then it must divide a factor of the product [Euclid's Lemma]
45127
Why is Euler's totient function equal to $(p-1)(q-1)$ when $N=pq$ and $p$ and $q$ are prime in a clean intuitive way?
15436
Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
10514
Proof that no polynomial with integer coefficients can only produce primes
146851
Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$
128575
Elementary proof that $3$ is a primitive root of a Fermat prime?
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
70406
Find all values x, y and z which satisfy the equation $(x^2 + 1)(y^2 + 1) = z^2 + 1$ given that $(x^2 + 1)$ and $(y^2 + 1)$ are both primes.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
38419
Existence of Polynomial with whom product contains only prime powers
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
103499
$x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
137230
Find all pairs of primes $p,q$ such that $pq \mid 2^p +2^q$