MathDB

17

Part of PEN G Problems

Problems(1)

G 17

Source:

5/25/2007
Suppose that p,q∈Np, q \in \mathbb{N} satisfy the inequality exp⁡(1)⋅(p+q−q)2<1.\exp(1)\cdot( \sqrt{p+q}-\sqrt{q})^{2}<1. Show that ln⁡(1+pq)\ln \left(1+\frac{p}{q}\right) is irrational.
inequalitieslogarithmsIrrational numbers