Questions tagged [nt.number-theory]

In a very helpful answer by Thurmond (A weighted sum over squarefree numbers involving Bernoulli numbers), Thormund reduces the problem to controlling the integral on the shifted line $\Re z=-3/2$, ...

Let $h(n)$ be the function that returns the minimum exponent in the prime factorization of $n$. We adopt the convention $h(1) = \infty$, so $1/h(1) = 0$. According to the abc conjecture, there should ...

Conjecture: Let $x$ and $y$ be integers such that $1 < x < y$ and $\gcd(x, y) = 1$. There always exists at least one prime $p$ of the form: $$p = n \cdot x + m \cdot y$$ where $n, m \ge 1$ are ...