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China Team Selection Test 2015 TST 1 Day 2 Q1

Source: China Hangzhou

March 14, 2015
algebraTrianglesgeometryChina TST

Problem Statement

Prove that : For each integer n≥3n \ge 3, there exists the positive integers a1<a2<⋯<ana_1<a_2< \cdots <a_n , such that for i=1,2,⋯ ,n−2 i=1,2,\cdots,n-2 , With ai,ai+1,ai+2a_{i},a_{i+1},a_{i+2} may be formed as a triangle side length , and the area of the triangle is a positive integer.
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