MathDB

Let

\mathbb{Z}^{+}

be the set of positive integers. a) Prove that there is only one function

f:\mathbb{Z}^{+} \rightarrow \mathbb{Z}^{+}

, strictly increasing, such that

f(f(n))=2n+1

for every

n\in \mathbb{Z}^{+}

. b) For the function in a. Prove that for every

n\in \mathbb{Z}^{+}

\frac{4n+1}{3}\leq f(n)\leq \frac{3n+1}{2}

c) Prove that in each inequality side of b the equality can reach by infinite positive integers

n

Problem Statement