MathDB

All positive integers

Source: French TST 2005 pb 4.

May 27, 2005

floor functionceiling functioninductioninequalitieslogarithmsnumber theory unsolvednumber theory

Problem Statement

Let

X

be a non empty subset of

\mathbb{N} = \{1,2,\ldots \}

. Suppose that for all

x \in X

4x \in X

and

\lfloor \sqrt{x} \rfloor \in X

. Prove that

X=\mathbb{N}