Given polynomial $f(x,y)$ with integer coefficients, may be reducible, but without linear factors. For positive integer $n$ denote by $a_n$ the number of points $(x,y)\in \frac1n \mathbb{Z}^2$ on a curve $f(x,y)=0$. May it appear that $a_n$ tends to infinity when $n$ increases?
many rational point on an algebraic curve
Fedor Petrov
- 108.9k
- 9
- 264
- 459