For prime $p$ and $q$, $2p^2=1+q^2$ are there many solutions?
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
131141
Solutions to $p+1=2n^2$ and $p^2+1=2m^2$ in Natural numbers.
97021
Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$?
20881
Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
20034
Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
4943
If $p,q,r$ are all primes,and $p|qr-1$,$q|pr-1$ and $r|pq-1$,find all possible values of $pqr$.
147307
How to evaluate $\sum_{\gcd (p,q)=1} \frac{1}{p^2q^2}$?
143194
How would you solve the diophantine $x^4+y^4=2z^2$
112390
Solutions of $x^2 \equiv 1 \pmod N$
119630
For an odd prime $p$, $\;p =1 \pmod 4,\; \;x^2+1 = 0 \pmod p$
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
117132
Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$
29811
Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$