A1:
((255 * 256) + 1) * ((255 * 256) + 1) = ((255 * 255) * ((256 * 256) + 1)) + (256 * 256)
;
(3 |^ (256 * 64)) * (3 |^ (256 * 64)) =
3 |^ ((256 * 64) + (256 * 64))
by NEWTON:8
.=
3 |^ (256 * (64 + 64))
;
then (3 |^ (256 * 128)) mod (Fermat 4) =
((673 * 97) * (673 * 97)) mod (Fermat 4)
by Lm45, NAT_D:67
.=
256 * 256
by A1, Th54, NAT_D:def 2
;
hence
(3 |^ (256 * 128)) mod (Fermat 4) = 256 * 256
; verum