MathDB
Clearing numbers and writing their difference

Source:

June 14, 2006
modular arithmeticinvariantinductionarithmetic series

Problem Statement

The numbers 1,2,...,19701,2,...,1970 are written on a board. One is allowed to remove 22 numbers and to write down their difference instead. When repeated often enough, only one number remains. Show that this number is odd.