Absolutely small solutions to a hyperelliptic congruence
Volume 166 / 2021
Colloquium Mathematicum 166 (2021), 335-340
MSC: Primary 11A05, 11A07, 11A15.
DOI: 10.4064/cm8340-3-2021
Published online: 11 October 2021
Abstract
We investigate the hyperelliptic congruence $$y^2\equiv (x+1)(x+2)\cdot \ldots \cdot (x+l)\pmod {m}$$ and ask whether there exists a constant $C(l)$ such that for any $m$ there is a solution $x,y$ satisfying $0\leq x\leq C(l)$. We prove that such a $C(l)$ does exist if we allow only prime modules $m$ but does not exist for general $m$.
