MathDB

40

Part of PEN O Problems

Problems(1)

O 40

Source:

5/25/2007
Let XX be a non-empty set of positive integers which satisfies the following: [*] if x∈Xx \in X, then 4x∈X4x \in X, [*] if x∈Xx \in X, then ⌊x⌋∈X\lfloor \sqrt{x}\rfloor \in X. Prove that X=NX=\mathbb{N}.
floor functioninductionlogarithms