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Lattice triangles whose centers are lattice points

Published 27 Apr 2026 in math.GM | (2604.25956v1)

Abstract: We show that for an integer $\ell$, there exists an acute integer lattice triangle of lattice perimeter $\ell$ such that its orthocenter is an integer lattice point, if and only if $\ell=6 $ or $\ell\ge 8$. Analogous results are obtained for the circumcenter and the centroid, and the results are contrasted with those for obtuse and right triangles.

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