[math-fun] computer word sizes of 2^2^n
6 Jul
2016
6 Jul
'16
2:14 p.m.
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?
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Henry Baker