Irrational Numbers arising from Certain Differential Equations
M. Ram Murty, V. Kumar Murty · Canadian Mathematical Bulletin · 1977
Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven's proof to show that er is irrational for every non-zero rational r. Dixon [1] made a similar modification to show that π is not algebraic of degree 2. In this note, we prove a general theorem which gives Niven's and Koksma's results as easy corollaries. A suitable modification in our proof also gives Dixon's result.