MathDB

2^{n-1}+n numbers can be chosed from the set

Source: Baltic Way 2001

November 17, 2010

number theory proposednumber theoryCombinatorial Number Theory

Problem Statement

Let

n

be a positive integer. Prove that at least

2^{n-1}+n

numbers can be chosen from the set

\{1, 2, 3,\ldots ,2^n\}

such that for any two different chosen numbers

x

and

y

x+y

is not a divisor of

x\cdot y