All Questions

Let $P$ be a polynomial having integer coefficients (and degree $\geq 3$), and let $\mathscr P_P$ be the set of prime numbers dividing some value $P(n)$ with $n \in \mathbb Z$. Is it true that $\...

According to Lemke-Oliver, irreducible quadratic polynomials $G$ with positive leading coefficient and $\rho(2)<2$, (where $\rho(m)$ denotes the number of incongruent solutions to the congruence $G(...

The starting point for this question is the following (false) statement $\forall n\in \mathbb{N} (n^2 + n + 41 \text{ is prime}).$ Given a polynomial function $p:\mathbb{N} \to \mathbb{N}$ ...

For motivation and related questions, see below. Rough sketch of the question. View $\bigsqcup_{p \text{ prime}} (\mathbb{Z}/p\mathbb{Z})$ as a ‘subset’ of the unit circle, via $a\pmod{p} \mapsto e^{...

Let $P$ be the set of all positive primes. Let $S$ an arbitrary infinite subset of $P$ satisfying the following assumption: there exists a finite Galois extension $K$ of $\mathbb{Q}$ and a conjugacy ...