MathDB

An estimate

Source: Indian Postal Coaching 2005

September 23, 2005

combinatorics unsolvedcombinatorics

Problem Statement

Let

a_1 < a_2 < .... < a_n < 2n

ne

n

positive integers such that

a_j

does not divide

a_k

or

j \not= k

. Prove that

a_1 \geq 2^{k}

where

k

is defined by the condition

3^{k} < 2n < 3^{k+1}

and show that it is the best estimate for

a_1

Back to Problems View on AoPS