[math-fun] computer word sizes of 2^2^n

6 Jul 2016

      Is it just me, or does anyone else find this property pretty cool:

(%i1) x^256-1,factor;
                        2        4        8        16        32        64        128
(%o1) (x - 1) (x + 1) (x  + 1) (x  + 1) (x  + 1) (x   + 1) (x   + 1) (x   + 1) (x    + 1)

I.e., the factors of 2^2^n-1 are (2^n-1) and (2^2^k+1) for k<n.

This property has to be useful for some recursions on computer word sizes, but I don't recall Knuth using it anywhere.

Is anyone aware of *any* interesting use of this property?

[math-fun] computer word sizes of 2^2^n

Henry Baker