A1:
282 * 282 = (1 * ((256 * 256) + 1)) + (71 * 197)
;
(3 |^ 256) * (3 |^ 256) =
3 |^ (256 + 256)
by NEWTON:8
.=
3 |^ 512
;
then (3 |^ (256 * 2)) mod (Fermat 4) =
(282 * 282) mod (Fermat 4)
by Lm39, EULER_2:9
.=
71 * 197
by A1, Th54, NAT_D:def 2
;
hence
(3 |^ (256 * 2)) mod (Fermat 4) = 71 * 197
; verum