A1:
(81 * 809) * (81 * 809) = (((256 * 255) + 241) * ((256 * 256) + 1)) + 64
;
(3 |^ (256 * 8)) * (3 |^ (256 * 8)) =
3 |^ ((256 * 8) + (256 * 8))
by NEWTON:8
.=
3 |^ 4096
;
then (3 |^ (256 * 16)) mod (Fermat 4) =
((81 * 809) * (81 * 809)) mod (Fermat 4)
by Lm43, EULER_2:9
.=
64
by A1, Th59, NAT_D:def 2
;
hence
(3 |^ (256 * 16)) mod (Fermat 4) = 64
; verum