On the congruence $f(x)+g(y)+c\equiv 0\ ({\rm mod}\ xy)$, II (the quadratic case)
Volume 184 / 2018
Acta Arithmetica 184 (2018), 1-6
MSC: 11D09, 11D25, 11D41.
DOI: 10.4064/aa8449-7-2016
Published online: 22 January 2018
Abstract
The congruence given in the title is studied for $f(x) = ax^2 + a_1x \in \mathbb Z[x]$, $g(y) = by^2 + b_1y \in \mathbb Z[y]$, $c\in \mathbb Z\setminus \{0\}$ and with either $|ab|=1$, or $ab\ne 0$ and $\mathop{\rm Rad} c\mid(a_1,b_1a)$.
