Abstract
Let k be a number field with algebraic closure k̅, and let S be a finite set of primes of k containing all the infinite ones. Let D be a nonzero effective divisor on ℙ2, at least one of whose irreducible components is a line nondegenerate on 𝕊1×𝕊1. Then we will prove that the set of (D, S)-integral points on ℙ2 (k̅), which are preperiodic with respect to the squaring map, is not Zariski dense in ℙ2.
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