query: Find all primes such that $x^{2} = -1$ has no solution in $\mathbb{F}_p$
positive_passages.docid: 18053
positive_passages.text: Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
negative_passages.docid: 126494
negative_passages.text: Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
negative_passages.docid: 153294
negative_passages.text: What is the infinite product of (primes^2+1)/(primes^2-1)?
negative_passages.docid: 154360
negative_passages.text: Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
negative_passages.docid: 38498
negative_passages.text: Find all primes $p$ such that $(2^{p-1}-1)/p$ is a perfect square
negative_passages.docid: 21862
negative_passages.text: Proof of lack of pure prime producing polynomials.
negative_passages.docid: 131385
negative_passages.text: How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
negative_passages.docid: 38419
negative_passages.text: Existence of Polynomial with whom product contains only prime powers
negative_passages.docid: 50596
negative_passages.text: $p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
negative_passages.docid: 54192
negative_passages.text: Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
negative_passages.docid: 144851
negative_passages.text: For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
negative_passages.docid: 53139
negative_passages.text: How to demonstrate that there is no all-prime generating polynomial with rational cofficents?
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 65511
negative_passages.text: Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
negative_passages.docid: 151961
negative_passages.text: Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
negative_passages.docid: 5978
negative_passages.text: Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
negative_passages.docid: 45882
negative_passages.text: Solving a congruence without Fermat's little theorem