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China Team Selection Test 2015 TST 1 Day 1 Q2

Source: China Hangzhou

March 13, 2015
number theoryinequalitiesChina TST

Problem Statement

Let a1,a2,a3,⋯a_1,a_2,a_3, \cdots be distinct positive integers, and 0<c<320<c<\frac{3}{2} . Prove that : There exist infinitely many positive integers kk, such that [ak,ak+1]>ck[a_k,a_{k+1}]>ck .
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