Problem 4

Part of 1991 French Mathematical Olympiad

Problems(1)

if x∈A then 2x∉A, maximize |A|

Source: France 1991 P4

p

be a nonnegative integer and let

n=2^p

. Consider all subsets

A

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

with the property that, whenever

x\in A

2x\notin A

. Find the maximum number of elements that such a set

A

Setsnumber theory