On certain plane curves with many integral points
Rodriguez Villegas, Fernando ; Voloch, José Felipe
Experiment. Math., Tome 8 (1999) no. 4, p. 57-62 / Harvested from Project Euclid
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We define a sequence of polynomials $P_d \in \funnyZ[x,y]$, such that $P_d$ is absolutely irreducible, of degree d, has low height, and has at least $d^2+2d+3$ integral solutions to $P_d(x,y)=0$. We know of no other nontrivial family of polynomials of increasing degree with as many integral solutions in terms of their degree.
Publié le : 1999-05-14
Classification:  14G05,  11G30 
@article{1047477112,
     author = {Rodriguez Villegas, Fernando and Voloch, Jos\'e Felipe},
     title = {On certain plane curves with many integral points},
     journal = {Experiment. Math.},
     volume = {8},
     number = {4},
     year = {1999},
     pages = { 57-62},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047477112}
}

Rodriguez Villegas, Fernando; Voloch, José Felipe. On certain plane curves with many integral points. Experiment. Math., Tome 8 (1999) no. 4, pp.  57-62. http://gdmltest.u-ga.fr/item/1047477112/