A1:
(71 * 197) * (71 * 197) = (2985 * ((256 * 256) + 1)) + (32 * 257)
;
(3 |^ (256 * 2)) * (3 |^ (256 * 2)) =
3 |^ ((256 * 2) + (256 * 2))
by NEWTON:8
.=
3 |^ 1024
;
then (3 |^ (256 * 4)) mod (Fermat 4) =
((71 * 197) * (71 * 197)) mod (Fermat 4)
by Lm41, EULER_2:9
.=
32 * 257
by A1, Th59, NAT_D:def 2
;
hence
(3 |^ (256 * 4)) mod (Fermat 4) = 32 * 257
; verum