http://opendatastructures.org/ods-java.pdf Page 132, Exercise 5.10 of the given pdf

We consider 2^W - 1 for some positive integer W. prove that, for a positive integer x, ((x mod 2^W) + (x div 2^W) x) (mod (2^W - 1)) The above equation can be interpreted and represented as follows: ((x mod 2^W) + (x div 2^W)) mod (2^W - 1) = x mod (2^W - 1) We recall that in a general formulation of equality mod z: x y (mod z) where x, y, z are integers, means that an integer k for which x = y + k z