A1:
(32 * 257) * (32 * 257) = (1031 * ((256 * 256) + 1)) + (81 * 809)
;
(3 |^ (256 * 4)) * (3 |^ (256 * 4)) =
3 |^ ((256 * 4) + (256 * 4))
by NEWTON:8
.=
3 |^ 2048
;
then (3 |^ (256 * 8)) mod (Fermat 4) =
((32 * 257) * (32 * 257)) mod ((256 * 256) + 1)
by Lm41, Th54, NAT_D:67
.=
81 * 809
by A1, NAT_D:def 2
;
hence
(3 |^ (256 * 8)) mod (Fermat 4) = 81 * 809
; verum