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Maximum number of regions after p-secting sides of triangle

Source:

February 11, 2011
modular arithmeticcombinatorics unsolvedcombinatorics

Problem Statement

Let p3p\ge 3 be a prime number. Each side of a triangle is divided into pp equal parts, and we draw a line from each division point to the opposite vertex. Find the maximum number of regions, every two of them disjoint, that are formed inside the triangle.