Proof of no primes such that $x^2 + y^2 = z^2$
43178
Why can't prime numbers satisfy the Pythagoras Theorem? That is, why can't a set of 3 prime numbers be a Pythagorean triplet?
73095
Foundational proof for Mersenne primes
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
18302
List the primes for which the following system of linear equations DOES NOT have a solution in $\mathbb{Z}_p$
53139
How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
152167
Prove that if $x,y,z$ are integers such that $x^2+y^2=z^2$, then $xyz \equiv o \pmod{60}$.
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
54359
Odd Primes Problem Proof
23099
Verifying that the ideal $(x^3-y^2)$ is prime
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
71756
diophantine equation: $x^2 +y^2 = z^n$
131731
Primes that can't be written as sum of two squares. Mod
155743
Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$