MathDB

4

Part of 2005 France Team Selection Test

Problems(1)

All positive integers

Source: French TST 2005 pb 4.

5/27/2005
Let XX be a non empty subset of N={1,2,…}\mathbb{N} = \{1,2,\ldots \}. Suppose that for all x∈Xx \in X, 4x∈X4x \in X and ⌊x⌋∈X\lfloor \sqrt{x} \rfloor \in X. Prove that X=NX=\mathbb{N}.
floor functionceiling functioninductioninequalitieslogarithmsnumber theory unsolvednumber theory