3 problems

Let $f\in\mathbb{Z}[x]$ be a polynomial of degree greater than one, and let $A_f=(f(1),f(2),f(3),\ldots)$ be its associated integer sequence. Write $g_f=g_{A_f}$, where $g_A$ is th…

Let $L$ be a primitive Gaussian line, meaning a line in the complex plane containing two, and hence infinitely many, coprime Gaussian integers. Let $g_L$ be the smallest positive i…

Pairwise coprimality conjecture. For any two different primes $p$ and $q$, the terms $u_p$ and $u_q$ are relatively prime: