The Exact Value f(8) = 17 in Erdős Problem #506
Year: 2026
Type: preprint
Abstract: We determine the exact value of the eight-point case of Erdős Problem #506, under Elliott's non-degeneracy convention that the points are neither all collinear nor all concyclic. We exhibit an explicit configuration of eight points determining exactly 17 distinct proper circles and prove that no admissible configuration can determine 16 or fewer circles. Hence f(8)=17. The accompanying verification package contains exact symbolic verification of the construction and independent computational checks of the most delicate combinatorial lemmas. This is priority version v0.1 and has not yet been peer reviewed.
Author: Zarzycki, Mateusz
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203708537
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