MathDB

8

Part of 2009 Junior Balkan Team Selection Tests - Moldova

Problems(1)

Prove that the greatest solution $n$ of the inequation $c_n<2009$ is a prime

Source: Moldova JTST 2009

5/10/2023
Side of an equilatreal triangle has the length n∈N.n\in\mathbb{N}. Each side is divided in n n equal segments by division points. A line parallel with the third side of the triangle is drawn through the division points of every two sides. Let cnc_n be the number of all rhombuses with sidelength 11 inside the initial triangle. Prove that the greatest solution n n of the inequation cn<2009c_n<2009 is a prime number.
combinatorics