Determining Decimal Expansion without Division
Source: 1988 IrMO Paper 1 Problem 11
September 28, 2017
Problem Statement
If facilities for division are not available, it is sometimes convenient in determining the decimal expansion of , , to use the iteration x_{k+1}=x_k(2-ax_k), k=0,1,2,\dots , where is a selected “starting” value. Find the limitations, if any, on the starting values , in order that the above iteration converges to the desired value .